I absolutely love battlemage builds, but I can understand your problem. Before anything else, I want to say this: I personally prefer battlemages in exclusively heavy armor and I detest the idea of using an Altmer in heavy armor, so neither will any of my build ideas use Altmer nor light armor.
First and foremost, we have a stamina problem. Yes, Respite is a great perk, but with only 100 stamina, we'll be using it often, and therefore using our magicka. Not a good idea in my opinion to rely solely on this perk, though it may be worth investing in.
Secondly, the price you pay for armor is that you don't get the awesome bonuses robes get unless you are a good enchanter or happen to have loads of money and good luck.
Generally speaking, Enchanting is a good skill for a battlemage. It mitigates the fact that you have to spread your attributes thin while giving you access to defensive bonuses, spell cost reduction, magicka regen and enchantments on weapons that reflect or compliment the magic you use in battle.
For balance's sake (and also so that we can have some other skills), Enchanting should not be used in conjunction with other crafting skills. I will not make examples of or advocate such builds. For a battlemage, Enchanting is the most useful crafting skill (as outlined above), so my builds and builds I will suggest will contain either Enchanting or no crafting skill.
As for the spell schools you use, that's totally up to you, but I have my suggestions. I speak from experience when I say that Destruction and One Handed compliment each other for the absolute most potent combat capacity I've seen in the game, so I implore you to try it. That, and it really suits the playstyle

However, it's perfectly reasonable that other players have used builds that completely mastered Conjuration, a melee skill, and sometimes added Archery. Those three skills combined with an armor skill and Restoration end up great: you'll have a tanky character who summons one- or two-handed weapons for melee, bows for range, atronachs, dremora lords, and even raises his fallen foes to fight for him. It's a really great build that I recommend, but it's not my style. Here's an example build that will hopefully interest you: http://skyrimcalculator.com/#135551
I left many things out of the build, most notably the Master Conjuration perk, but I assure you that it works very well. Atronachs and weapons for every occasion, generally a free hand for casting, powerful healing and necromancy, this build pretty much has it all. But, as I've said, I'm more fond of using Destruction, so on to that.
----------
For the sake of preparedness, I prefer One Handed to compliment Destruction, though I would neither invest in dual casting nor in dual wielding.
Important note: A lot of people are saying that you should invest in only one element if you use Destruction in a battlemage build to save perks. This can be a good or a bad thing depending on how you do it. I advise you to invest your elements with the following in mind.
Shock is the best element for neutral coverage. The pros are that very few enemies resist it, it travels instantaneously, it harms enemy spellcasters significantly, and it can turn enemies to ash. Disintegrating enemies is more than a gimmick: on top of being an automatic one-hit kill when they're at low health (meaning you can cast a menial lightning spell at an enemy at low health to kill them instantly while not spending a lot of magicka), there's no corpse for an enemy mage to raise. This can be greatly important, as when you're fighting a group of strong mages, you usually end up fighting them twice, which is not something anyone is overly fond of doing. However, this leads me to the cons of shock damage.
Firstly, just as stated above, it disintegrates enemies, which leaves you with two problems if you're using Conjuration: either you can't reliably invest in the necromancy branch of the tree, or you can't use shock spells to their full potential. Secondly, shock is the most expensive element, which is never good. Finally, while excellent neutral coverage is a good thing, it's also a bad thing--just as few enemies are resistant to shock, there are also few (if any) that are weak to it. Currently, I know of no enemies weak to shock damage.
At the end of the day, shock is still superior to the other elements in terms of singular usage. If you're going to go for one, go for shock.
Fire and frost, though, have their pros as well, and in fact I prefer them to shock. Alone, they're not as potent--you'll find that there are resistant enemies all over Skyrim and that their secondary effects aren't great on their own, and half the dragons you fight will resist your magic by 50% if you choose only one of these elements (as opposed to dragons being neutral to shock damage). However, fire and frost synergize extremely well and do better together than shock does on its own--for the cost of twice the perks, of course.
For starters, fire and frost together have the best coverage you can get. Aside from one enemy (some mage, there's only one of him) who is almost immune to all magic and shouts, you'll be hitting things hard: fire and frost is the best super effective coverage in the game. Almost every enemy you encounter, including dragons, will either be weak to one of the two or neutral to one. Without the top perk in their branches, fire can already set up enemies for further damage and frost can slow enemies and prevent them from power attacking with its stamina damage. With the top perk, you're looking at casting a fear effect with no level cap on
any enemy short of dragons and paralysis. Those five status effects--fear, slow, paralysis, stamina damage, and extra damage while on fire--are useful against any enemy it can affect (read: the majority of enemies), versus shock's single status effect of damaging magicka (which is only useful against enemies who cast spells) and its chance to disintergrate foes (which is only useful against mages who raise undead). Finally, both elements are less expensive than shock.
It is obvious to me that fire and frost together are superior to shock, and that shock is the best element on its own. Investing in all three can make for a powerful mage, but we generally cannot spare the perks, especially with a hybrid build like this. Also, remember that, if you invest in Enchanting, your weapon enchantments will benefit from your Destruction damage perks--another reason to use fire and frost over shock alone, as you'll be saving more perks and doing more damage with better effects using a build that contains this (http://skyrimcalculator.com/#135557) rather than this (http://skyrimcalculator.com/#80033). At the end of the day, though, it's all up to you which element(s) you choose.
----------
Restoration is pretty much a must-have for battlemages. I don't think I need to explain why. Conjuration and Illusion are options, though not necessary. Within Conjuration, when it comes to which allies you want on the field, you should have EITHER this (http://skyrimcalculator.com/#80033) OR this (http://skyrimcalculator.com/#80033). One rank in the Summoner perk is necessary to get the higher tiered perks on the atromancy branch, and it's certainly not useless (I'd say it's a lifesaver), but two ranks is a bit much and is wasteful in my opinion.
For atronachs, dual casting is not necessary as you can simply summon them again (and they're likely to die at lower levels or against tougher enemies before their time would expire twice over, anyway). For risen dead, however, dual casting is imperative: only staves, the Ritual stone power, and Dead Thrall can raise zombies that don't disintegrate, so it's highly important that we use dual casting to lengthen their, uh, lifespan. Even when you can cast Dead Thrall, it only works on humanoids, who not only might not be present (say, in a draugr crypt), but may not even be the best choice (is that a dead mammoth right next to you?).
Whatever you do with Conjuration, I advise against getting the master perk for many reasons. Firstly, you may just not want a permanent ally: different situations call for different battle tactics, and it would be especially disappointing if you spent a perk, casting time, and lots of investment in magic and cost reduction to summon a permanent Storm Thrall just to find out that you'd be better off with a Fire Atronach for a fight. Secondly, even if and when you do want to summon a permanent or semi-permanent ally, there are better ways to do it than wasting a perk. Consider that, of all the master spells in all schools, it's generally an infrequent thing and always better to do outside of combat, so you can easily just find the resources (magicka + cost reduction) to cast the spell at your leisure rather than spend a perk on it to cast it cheaply.
Finally, there's Illusion. I don't think it's incredibly useful for a battlemage, but if you want, you can do this (http://skyrimcalculator.com/#135564). Eight perks is pricey, but this allows you to cast Muffle and Invisibility in order to add some stealth to your playstyle--and I don't mean for assassinations, but for getting the hell out of the battlefield. Useful, yes, but not incredibly important, especially since Restoration and Heavy Armor generally keep you healthy and Respite allows you to run away pretty easily. Using Illusion for the only other thing it does, battlefield control, requires practically every perk in the tree to be effective. Is it useful? Incredibly so. Is it worth it? Not for a build that doesn't specialize in it, and most certainly not for someone who already has a powerful presence on the battlefield.
----------
Here are a few sample builds. They're based on one overall build that's tweaked for different playstyles.
With Enchanting, specializing in fire and frost: http://skyrimcalculator.com/#80033
(Big, angry, bulky damage dealer. Freakin' unstoppable and generally my favorite battlemage build.)
Non-elemental Enchanting with fire, frost and Necromancy: http://skyrimcalculator.com/#80033
(Remember, kids: no shock + necromancy.)
Heavy Elemental Battlemage with no Enchanting: http://skyrimcalculator.com/#80033
(Atronachs and no Enchanting give us room to use all the elements and use Heavy Armor to its fullest potential [useful for falling off cliffs, running around, and punching people].)
Enchanting, all elements, no Conjuration: http://skyrimcalculator.com/#80033
(Pretty well balanced.)
That's all for now. I'll edit this post as necessary.
PLEASE NOTE: It's four in the morning as I write this in my part of the world. I am tired. It is perfectly possible that I messed up some of the builds and left perks in there that I didn't mean to. I'll come back here tomorrow to look over my post and edit anything that needs it.
I hope I managed to help!
