the marvel ultimate alliance 2 online co-op save system works like this:
Each person works with their own save file which contains their overall stats/challenges, difficulty level, and last checkpoint reached on the map. In order to gain experience for your characters you have to play on the same difficulty as the person hosting. Otherwise you can only get collectibles.
All experience gained on the online hosts save file is shared among all characters. If you earn 1000 exp, each character in the party can use that experience. As a guest to the host any experience that I spend on the character I'm playing as will be added to only his save. In other words when you switch over to your save after leaving the co-op session that 1,000 experience will be carried over for you and you will have to spend it again on your characters stats for your save file.
*Edit: Also you can't join a co-op game with someone who is farther ahead then you and get stats and experience. Only collectibles will count here too. You can join a game with someone who is farther behind and get everything though.
