What is the ruling regarding my Muslim husband taking out an interest-bearing loan from a non-Islamic financing company, with his agreement with a non-Muslim merchant (his friend) that the merchant will pay the interest accrued on the loan, while my husband pays only the principal amount?

Your husband is not permitted to enter into a usurious loan agreement with a financing company, even if his non-Muslim friend is the one who will pay the interest. A Muslim is not allowed to engage in prohibited contracts like usury (riba), because doing so implies an affirmation and acceptance of usury, which is forbidden. Dealing with usury or assisting in it is not permissible.