Please be aware that if you are married and living in the same house, that his credit rating would affect your credit rating too. Even if you keep your finances separate. The only way to stop him getting another card is to let him (and you) get bad credit. If you bail him out to keep your own slate clean then he can continue to get cards.

There are ways you can find out if there have been any credit checks done on your name and address, which are necessary for any new credit. Keeping an eye on this might be one way to find out if he is applying for new credit, although having to resort to that sort of snooping may obviously not be good for your marriage. Good luck.