Hey, I don't think you need to download a Dlc to play campaign.
I think I have the solution: 1. Install the game (press X on the dashboard option where you would usually press A to play the game/open or close tray).
2. Then go to your storage device your halo memory is on and delete all your memory of halo 4 and also clear system cache.
3. Finally, Install the game, do the update and your campaign should work.