Call of Duty: Infinite Warfare will not include Co-Op Campaign.

So it turns out that Call of Duty: Infinite Warfare will not include Co-Op Campaign like Black Ops 3 did with it’s 4 player feature. However, Activision confirmed co-op will be limited to Infinite Warfare’s Zombies mode.So this makes Zombies the only place where you can play with your buddy besides regular multiplayer. This new Zombies mode by Infinity Ward will actually have a story line and unique mechanics, we will hear more about this feature later this year.
Infinite Warfare delivers three unique game modes: Campaign returns to the gritty, large-scale war roots of the franchise, while boldly looking ahead. Multiplayer delivers the future of warfare, with many new gameplay innovations. And the cooperative Zombies mode takes players on a wild ride through a new storyline with unique gameplay features and mechanics.
Infinite Warfare is due to launch on November 4th, 2016 for PlayStation 4, Xbox One, and PC.

Source