Curious as to how you are trying to connect. A friend of mine and I went through a lot of trail and error with game settings and the way we thought that you get into a co-op game. We eventually were able to do it but it was not the "normal' procedure you might think. We played in the "Freeplay" mode set to "Private" and set a password. I was both able to invite him and he was also able to find my game if you set the "Search Internet" to Search for Friends. Had no problems after that.
Oh, there was one thing which we dod not try and that was level of characters being different. He had tried to join my game with a higher level character and was unable. So, he created a new character and at first we still had problems. Once we did the above, we where able to connect to each other but did not try with different level characters. I did notice that their is a setting in there somewhere that lets you set server preferences to something like "Old school" which allows players to join at your level or higher.
We are trying to play the Campaign in Co-op: So it goes something like this: I start a game by clicking Campaign > I select First Map > Visibility: Private > Set Password. Co-op is preset, since thats the only multiplayer mode available for Campaign. Then I select Difficulty : Easy, Rank Restriction : My Rank or Higher, and click Start Game. Once the option appears, I click "Show Spawn Menu" and there is an Invite Friend button on that menu in-game. I click that and up pops my friends list with invite buttons by their names (A Steam window). I click "Invite" on a friend. My friend gets the game invite, and clicks it. A Steam server window shows up for my friend and it says: "Server Not Responding".
I think it is pretty clear this is a normal way to try to get multiplayer going, the most intuitive way I've found via in-game UI, at least for Campaign Co-op.