When it comes to finances in a joint capacity I don't think it is snooping at all. It is your right and responsibility to be informed about what you may be liable for, period.
However if he is opening up the credit card accounts in his name alone then leave it alone. It's not your problem and will only cause you more grief. Sometime I believe ignorance really is bliss. You can't make him stop getting the cards and maxing them out so as long as he is not putting you at financial risk...detach.