You are correct that money spent to keep up the payer's own property is not alimony. However, it depends on the language of the decree. If it says something like "[spouse 1] shall live in the marital home owned solely by spouse 2, and spouse 2 shall pay the mortgage and property taxes on the home until it is sold or spouse 1 moves out" then it is not alimony.
But if the decree says something like "[spouse 2] shall pay to spouse 1 $$$$ in spousal maintenance. Spouse 1 may live in the marital home provided that spouse 1 pays the bills." then the payment is all alimony and you just happen to be using it to keep living in one home rather than taking the same amount of money and moving to a different home.
Because divorces can be very complicated (and lawyers and judges often don't know or follow federal tax law very well), you may need to have your divorce order reviewed by a tax professional.
