Yes, a creditor can collect a marital debt from either spouse regardless of which spouse is ordered to pay the debt by the Court. The innocent spouse then has the right to recover from the obligated spouse, unless he or she files bankruptcy.
You and your spouse are responsible for community debts. The Court usually requires/orders one spouse or the other to pay certain community debts in, or through, the Decree of Dissolution or Legal Separation. A Court Order that does this is binding on the spouses only, not the creditors. You and your spouse are legally responsible for these community debts whether you are married, divorced or legally separated. These debts are matters of contract between both of you and your creditors (such as banks, credit unions, credit card companies, utility companies, medical providers, and retailers). On request, the Court may impose a lien against the separate property of a spouse to secure payment of certain community debts.