Perfect. Yeah, that's what I thought. I mean, if you can say "his and hers," then why wouldn't you be able to say "his and John's"? A part of me kept thinking it should be "It is he and John's couch" for some strange reason. I don't know why, since "his" is more logical.
A name might be better, depending on what came before it, yes. But if "Chris and John" was used a lot already, and Chris is being spoken of at the time, making it more than clear that "his" wouldn't be referring to anyone else, then, in that case, I'd go with "his."