Do I bear a sin if I use my husband's car that he bought with an interest-based loan, or if I am forced to pay its installments from my salary?

You did well to oppose your husband's borrowing with riba (interest). This is how a righteous wife should be. There is no harm in benefiting from the car purchased with an interest-based loan, because the prohibition of the loan is attached to the borrower's responsibility, not to the specific item for which it was used. Your husband must repent sincerely, and it is permissible for you to help him repay the principal of the loan, but not its usurious interest.