Is it permissible for my husband to fast while he experiences blood in his urine, which may continue for weeks after a prostate operation, knowing that he purifies himself for every prayer?

The emission of blood or urine after surgery does not affect the validity of the fast. Regarding your husband's situation, consider whether fasting would worsen his illness or delay his recovery, based on experience or the advice of a trustworthy doctor. If this is confirmed, then he is permitted to break his fast and make up for it later.