you cant play the normal campaign online but you can play spec ops with two people online
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There is no campaign for multiplayer. There is multiplayer which has no storyline, there is special ops where you can do co-op to do either a kind of campaign with a storyline with a friend or do survival mode to survive as many times as possible, or there is campaign mode, which is a single-player storyline.
No. The multiplayer is available straight away for you to play. The only things you can gain by finished the Black Ops campaign is the zombie map Five (which can also be unlocked by a cheat).
Go to "Special Ops" in your menu, rather than campaign or multiplayer, select 2 players then choose a mission. It's not a story based co-op, unfortunately.
You can not play split screen on multiplayer. It also left me confused
its called special ops