As far as Islamic Shari`ah is concerned, mortgages offered by Islamic banks are permissible. It should be stressed that the Shari `ah allows financing but prhibits interest. Therefore, a Muslim is allowed to take mortgages offered by Islamic banks if it takes one of the forms mentioned below.
Dr. Monzer Kahf, a prominent economist and counselor, states: Mortgages offered by Islamic banks are permissible according to Shari`ah. Financing is permissible in Islam whereas interest is prohibited. Interest is an increment in a loan. Financing may be done on the basis of a sale contract or ijarah (leasing) contract. In ijarah, the financier owns the property and collects rentals on the part he or she owns while also offering to sell its share in the property on installments to the occupant. There is nothing forbidden in this, especially when the contract itself is reviewed by respected Shari’ah experts as what Islamic banks usually do.
The same thing happens with sale financing, usually called murabahah. The bank purchases with you the property and sells you its share in it on installments at a higher price. This sale with a higher price is permissible as it is included in the implication of the text of the Qur’an itself (2:279).
Shari`ah prohibits increments in loans but does not prohibit financing itself. Therefore, once financing is done by means of sale and/or ijarah, it becomes permissible. The problem arises from similarities of both approaches in house financing. But to understand the purpose of the prohibition, you really need to look at cases of dissimilarities such as debt rescheduling or debt discounting.