Ok, I think I might have this co-op stuff down.
The book states that the only way to get achievements and to have items carry over, is to join someones game if YOUR progress is equal to or greater to theirs. Also, you need to be on the same side (pro or anti registration).
When I got the game tonight, I played up to the second level. I had some medals, the alternate hulk outfit, etc.
My friend started the co-op game from the beginning, and I loaded my save file. Obviously when I started, I didn't have any of my characters and they weren't leveled up.
However, we played past the second level (actually, we played for a good 4.5 hours

) and when we stopped, I saved my file on a separate slot.
Here's where it gets interesting. Not only did that file have a ton of experience, the medals I got in co-op and my deadpool alternate, but I also had all the medals from my previous file, along with my hulk alternate.
To sum it up, if you're going to join someones game, and you want to keep all your stuff + get more, you HAVE to join a game thats at the same point or before you. If you join a game at a point you haven't completed yet, I dont THINK you'll get achievements and items.
Hope this helps.