How gross is it to keep something that a cat peed on?

My roommate and I were taking care of a cat for a while who was kind of an asshole and peed on my bed repeatedly. I tried cleaning it with commercial cleaners, none of which really did the trick. The mattress continued to smell more than a little of cat pee. Finally, I flipped the mattress over and voilà: no more stench.

Nearly a week ago, I began the arduous process of moving, and when it came time to move my mattress, I re-learned that the pee side of it really stinks. And is visibly stained. With pee.

I tried again to clean it and left it out on the balcony to dry for a few days. These pee remnants are really going nowhere. Believe me, I have really tried everything at this point.

A friend who helped me disassemble my bed was horrified by the pee mattress and insisted I throw it out. I feel that my compromise of turning the mattress over is acceptable.

Am I mistaken? Am I living in filth? Is this so disgusting I should spend $180 or so on a new mattress? Please be honest. Don’t hold back. Thanks.