Yes, Battlefield V has co-op. It’s a four-player mode called Combined Arms, and it lets you dive into missions with your squad mates. Combined Arms missions are multi-objective battles, loosely based on the idea of infiltrating an area, completing several different tasks, and then extracting. Missions will be randomly generated each time, so you’ll be going for varying objectives and asked to do different things, potentially keeping it fresh every time you play.
You’ll be able to play with your created characters across all modes, including Combined Arms, and any rewards you earn will be usable across all modes too. DICE very much see Combined Arms as a bridge between single player and multiplayer.