You could ask for a modification of alimony, which is permissible and which the court may grant in some circumstances, but requesting a modification of alimony seems like the much more difficult route to take.
I would recommend filing a petition for contempt of court instead. If he is court ordered to pay the mortgage, and if he is not paying it, he is in violation of the court order and may likely be found in contempt. As part of the contempt finding, he will be ordered to pay the mortgage and possibly your attorney fees or other penalties in order to purge his contempt, and the court may schedule follow-up hearings to keep tabs on whether he is making his payments. This route is easier than filing a petition to modify alimony because it is much more straightforward and leaves less room for argument.
You probably want to talk to an attorney to help you through the process, regardless of which route you choose to take.
I hope this helps.