This is not possible. The only game I've ever played that allowed cross-platform multiplayer was Portal 2, which allowed co-op gameplay between users on Windows, Mac and PS3. Xbox 360 was excluded because Microsoft didn't allow it. There are other games with cross-platform gameplay, like Final Fantasy XIV, but I haven't played that beyond the beta.
I think cross-platform gameplay for a game like Mass Effect 3 could work between console players, but PC gamers are more skilled due to their mouse and keyboard setups. For this reason, PC players would not want to be teamed up with console players as this could cause friction. The aforementioned Portal 2 does not really have this problem, because players are allowed to take their time and don't require fast reflexes.
