All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There are two ways for purchasing a house or car through a bank.
Firstly, the bank actually purchases the house/car and then sells it to you for a higher value to be paid according to installment plan.
This, without a doubt, is lawful. It is called Al-Muraabahah in Islamic financial institutions.
Secondly, the bank does not actually purchase the house/car, but pays the value on your behalf and then demands you to pay the paid price plus the supposed interest. This, in fact, is forbidden and a kind of usury. This is the normal financial transaction dealt with in usury-taking banks.
Thereupon, it is forbidden for a Muslim to do such an action even though the monthly installment equals the monthly rental, since this transaction is a form of Riba (usury and interest) which opens a door to what is evil in this worldly life and in the Hereafter.
Allah knows best.