I've noticed a few characters (specifically Hadvar) who are equipped with light and heavy armor.

It's usually in the fashion of a set of light armor with a heavy armor shield. In Hadvar's case, he has the light Imperial Armor, but he also has a heavy Steel(or iron?) Shield. I also notice the Solitude blacksmith gives you a mixture of the two when you tell him you're a 'medium' fighter.

Will this level up both heavy and light armor? What are the advantages, if any, of doing this?

It will level both, but at a slower rate. Then you can't take advantage of many of the perks in each armor tree. I personally like making characters who use both types of armor.

I don't think sheilds count as armour? not sure if they do or not

hadvar acctullay switches to heavry armour if you meet him later during the imperial qeust line, likey to show that he has been promoted

Oh yeah now I remember, he does, that's right. I forgot.

I don't think Shields count as armor either... I just go to Whiterun and my heavy armor has not gone up any (I am using the iron shield you find in the torture chamber underneath Helgen).

Learn something everyday,

There are no advantages other than it looking cool.

I think shield-type is more of a preference from my 10 minutes of experience.

I wonder if it slows me down though.