It makes no difference if your credit card is under your name and your name only. If you acquired this debt during your marriage, it is a marital debt and a judgment creditor can pretty much locate any assets it can and get a lien, attachment or garnishment. So if you jointly own a savings account with your husband, that whole account is going to be frozen (in the entirety). Further, if you have other accounts (certificates of deposit, money market, savings, checking, etc) with the bank or any bank and the creditor finds it through background checks, that creditor will attach to all accounts and then begin the process of seeking wage garnishments.