If both the banks mentioned above build house or purchase the house and add some amount to the spent money (though in the name of interest) and then you purchase the house on the total amount which you will pay yourself in lump sum or instalments as per the dealing, then both the ways are permissible. In this way, buying a house from the banks is right. You should write clearly if there is any other way of purchasing a house.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband