The campaign is single player, but there is a two player co-op "story"-mode thing. You play it with 1 of 6 different characters that modify their race, adds powerful spells and has unlockable progress stuff. 3 of these 6 characters are free to play, if you just install SC2. Perhaps one person has to own the game though, not sure.
Today's post brought to you by the letter: "heck".