Courts do not generally regard the matrimonial home as an income source. Typically the matrimonial home is the only significant asset apart from pensions and more often than not the whole of the equity in that matrimonial home is required to provide for the housing needs of both spouses after divorce. If for some reason it is not possible to sell the matrimonial home immediately because, for instance, it is needed as the home of dependent children then it is usually possible to sell it later (for example when the children cease to be dependent) and to divide the equity at that stage.
It is not normally regarded as fair that one spouse should end up living in a mortgage free property while the other has to rent. More often than not that type of situation is only temporary (albeit one possibly lasting for years) until the former matrimonial home can be sold and the equity divided. It sounds as though you are looking at an unrealistic outcome.