The multiplayer portion of The Last of Us will not be campaign co-op, Naughty Dog recently told Gaming Examiner. The possibility of cooperative play hasn't been ruled out entirely, as the developer noted, "We're not ready to talk about the details of how multiplayer will be implemented, however we can say that it is not co-op within the main campaign."
It's still possible we'll see cooperative play offered in discreet episodes, as Naughty Dog did with the Uncharted series. Of course, there's the possibility for adversarial multiplayer as well, though that seems a bit ... inappropriate given the heavy subject matter in The Last of Us.