A Marital Settlement Agreement will not change a creditor's rights. In other words, simply because a settlement agreement says one party is responsible for a jointly titled debt, the creditor's rights to sue either party in the event of a default remains unchanged unless the debt is refinanced or otherwise modified as to remove the "not-responsible" party.
For example, if Husband takes house and mortgage (which are in both parties' names) and, prior to refinancing the mortgage, Husband defaults, that lender can go after both parties. Wife, assuming the settlement is worded correctly, can then go after Husband for his failure to do what he was supposed pursuant to the settlement agreement, and possibly recoup any expenses she is out-of-pocket due to his default.
The fact that they are medical bills seems kind of strange, as generally you would see those in one party's name. My guess is, maybe, that he was covered by your health insurance plan, which is why you'd be associated with those debts.
Gerald is correct. However, you have rights to enforce against your ex-spouse under the divorce decree to reimburse you and pay any and all costs and legal fees you incur because of his failure to abide by the divorce terms. You should consult a family lawyer in your area.
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