Is it permissible to reside and pray in a house that was purchased through an interest-bearing loan from the bank, and is prayer therein accepted?

If the husband purchased the house with an interest-based loan, without being in a state of necessity, then his action is forbidden, and he must repent. The prohibition of an interest-based loan pertains to his own liability, not to the money itself. Therefore, it is permissible for you to benefit from the house and pray in it. If the purchase was made through an Ijara-Muntahia-Bil-Tamleek (lease-to-own) contract, the ruling varies depending on the specific terms, but there is no harm in benefiting from it because the prohibition relates to his liability.