Arkane's upcoming Redfall, an open world cooperative FPS in which you and three friends shoot vampires, won't track missions you complete in a friend's game. So, if you join someone else's game and complete a mission, but haven't done it in your own world, you'll have to do it again when you host your own playthrough.
Crucially, however, Redfall will save character progress like experience and loot gained in players' campaigns. For many, that will be the only thing that matters.
It seems to be the case that, because it's an open world game, Redfall's designers didn't want the story to get broken up into chunks played out of order.
Game director Harvey Smith told IGN that "for the flow of things" players would have to redo missions they'd already done elsewhere. "The story would be very confusing if you got to mission eight and it said, 'skip this one because you've already done it.'"