Do I list the expense and leave secured claim blank since it’s not legally mine?

Your budget should include the debts you pay for reasonable living expenses. If your expenses do not allow you to make the GOOD FAITH TEST, your bankruptcy could be denied. Not having a payment on a car loan is often the difference in being eligible for bankruptcy and getting into trouble. I appreciate that it may be difficult to understand my answer. Which is why you need representation by an experienced attorney and not rely on free advice in an online forum.

In the bankruptcy petition, you disclose the property that you own (but not property owned by others) and you disclose the expenses for your household including everyone that lives there. So the car and debt loan secured by the car are not disclosed on your petition while the loan payments are disclosed on your petition.

Do you live in a community property state, like Wisconsin and about 10 others? If so the debt MAY be yours as well. The answer may depend on whether he acquired the car after the date of your marriage. You really should consult an experienced BR lawyer on your locality, who can explore all the facts and give you fully informed advice.