I don't think he would be allowed to get the benefit of council housing, if he's an American citizen. Maybe others can correct me if I'm wrong, but I thought that you weren't eligible for stuff like that (and jobseeker's allowance, etc.) unless you have indefinite leave to remain (and not just a spouse visa).
Since he's American and is here on a spouse visa, he is subject to immigration control. It means you have to have permission to be here, essentially.
That's my understanding, anyway!