There are a total of six campaign missions you must complete from start to finish on any difficulty with another player. You can complete this split-screen with a friend or a second controller if you do not have an active internet connection.
The missions do not have to be in order, you just have to load the mission from the start and play through to the end. If a player gets disconnected you will have to restart the mission from the beginning.
It also does not matter if you switch characters, switching characters is a pretty fun part of the game and can definitely help you out.
Also in case any one was wondering system link is not supported.