Unfortunately you are responsible for debts incurred in the marriage. Although the Court may require one party to pay a joint debt, that ruling does not prevent a creditor from pursuing either party for an unpaid debt. The creditor is not a party to the divorce action. The Court has no authority to modify the terms of the contract that was executed with the creditor.
If it were me and I could afford it, I would pay the debt or make arrangements to settle the debt with the creditor. If it is a revolving loan, I would make certain that the account is closed so that he can't keep running up the debt while not making any payments on the account. Then, I'd file a claim against him in court. The court I'd file in would depend on the dollar amount. If it is a lot of money, hire a lawyer. Once I got a judgment, I'd file a lien on any property he has of value so that when he went to sell it he'd have to pay me first out of the proceeds of the sale. If he owns real estate and an oil and gas leasing company wants to option his property to explore under his property, then they will have to pay the lien off for him before they can execute a lease with him.
Don't be a bitch. Just look at it as taking care of your business.
If you can't afford it, then that is a whole nother thing because you just can't squeeze blood out of a turnip. If the judge ordered him be responsible for the debt in the divorce decree, when the creditors call throw yourself on their mercy. Tell them the court ordered him responsible and you've got no money. Maybe they'll write it off. Again, if it is a lot of money, you will have to pay taxes on the amount written off as income.
Good luck to you.