What we understand from the question is that the bank sells its share of the house to you, and the price is divided into monthly instalments. But at the same time the bank retains its ownership of the house until the instalments are paid off, and during that period it rents its share of the house to you.
Based on that, you pay a monthly sum, part of which is towards the price of the house and the other part is rent for the house.
This is one of the kinds of “rent-to-own” schemes, and it is a haraam kind, because it includes a number of things that are contrary to sharee‘ah, namely:
1- It goes against the implication of the sale contract, because the sale contract implies that the item sold is transferred to the purchaser, but in this case the house remains under the ownership of the bank and is not transferred to the purchaser.
One of the statements of the Islamic Fiqh Council is that “the seller has no right to retain ownership of the sold item after the sale.”
Qaraaraat wa Tawsiyyaat Majma‘ al-Fiqh al-Islami, p. 110
2- It includes two transactions, namely sale and rental, concerning one item at the same time, but these are two different transactions. Sale implies that the item and its benefits are transferred to the ownership of the purchaser, who becomes liable for it and entitled to its benefits. Rental implies that the item remains the property of its owner and the renter is entitled to make use of its benefits only; he cannot dispose of the item itself. It says in a statement of the Islamic Fiqh Council: The reason for the prohibition of rent-to-own schemes is that they involve two different transactions at the same time concerning the same item. End quote.
See also the answer to questions no. 97625 and 125909
The way to get out of that is:
The bank should sell you its share of the house for monthly instalments, even if that is for more than the price for which it bought it, and it should make the house collateral until the instalments are paid off in full, so as to protect its rights.
And Allah knows best.
Reproduced from Islam QA