When I was dating a girl once we were sharing a bank acct. she owed tons to credit cards and loans etc and one of them put a freeze on our bank acct even though I wasn't on any of her loans or credit cards. Bank told me if we had been married then the creditors couldn't touch any joint accts. So I don't think they can really some after you for her accts.
If you are not on the card at all, they will try to tell you that you need to pay but it might not be true. In my state (Midwest) they tried it with me during my divorce and failed. My divorce lawyer did have to write them a letter before they stopped calling though.
I don't know if its true in NJ, but in many states each spouse's debt is his or her own. Unless both your names are on the account, they probably cannot hold you responsible. That doesn't mean they won't lie to you about it, though.