Source: 343 Industries
We have a new timeline after numerous delays for Halo Infinite's co-op campaign. 343 Industries hopes to release the feature sometime in August 2022. It was initially scheduled to arrive with the December 8 release date. This August schedule is meant for networking co-op, while split-screen co-op is expected to come later.
According to 343's roadmap, the couch co-op option won't be available until sometime in season 3, which isn't scheduled to start until November 8. But as Engadget pointed out, this is still a tentative plan, with the exact release date still marked as "TBD."