My husband is unemployed and holds a US greencard, I'm an employed US citizen and we have plenty of savings. We plan to travel together to visit friends and family in the UK and France for just one week with a return ticket. Is there a chance that he will be declined or will both our finances be looked at together when his visa application is reviewed?
It is absolutely usual that only one of a married couple is working. As long as you can afford the trip for both of you, and you fill in the appropriate forms to say you will be paying, then you will not be rejected on the grounds of finance.
There may of course be other issues that prevent you from getting a visa, but that will not be one.