Head of household does not mean you are the financial or moral head of the family. It is a special status for single parents who care for children, either because they are unmarried or because they have a long term separation from their spouse.
If you are separated from your spouse and correctly file as HOH, your tax refund is not subject to offset by your spouse's past debts.
However, if you are not separated, you can't file HOH. Your options are to
a. file married filing jointly, and include an "injured spouse" form
b. file married filing separately.
If you file as married filing separately, you report only your income, and your share of deductions and credits. Your tax refund is not subject to offset by your spouse's debts. If you file jointly, you list all your combined income and deductions on one tax return and you take joint responsibility for the taxes. Joint filing usually has lower taxes because some deductions and credits are limited when filing separately, but your joint refund is subject to offset. If the debts are from before your marriage, you can include an injured spouse form to request the IRS to consider your share of the refund as separate from your spouse's debt. But if the debts are from during the marriage, you are stuck paying them if you file jointly.
