I agree with Ghost. While it might be cool to meet up with one or two other teams, and conduct a synchronized assault on a base, the last thing I would want is for some yahoo to pop me in the back of the head, or wait until I'm in the middle of a base, and blow up a gas tank, sending the base into full alert, just for ****s and giggles.
Keep them totally separate. The biggest complaint about PvP being included in the game from PvE players was based on the fear that it would mean something like the Dark Zone in the Division. There is no way that a player should be able to come into your mission and wreck it even if that were unintentional let alone deliberate.