The host is the only one with the save files.
When you join him after he starts the game, you will take control of whichever character he is NOT controlling, so he needs to make sure he has the proper character active before you join.
If you cannot see his game, he may not have it visible in the options. You can choose whether you are Public, Friends Only, Invite Only, or Private.
Assuming you're on Steam, he can invite you into the game by Shift-Tabbing into the overlay and sending the invite from his friends list. Or, assuming he has the game as visible to Friends (or Public) you should be able to find it in the game list.
The invite method is probably the easiest, and also prevents accidental joins from strangers.