Wow. I have absolutely zero tolerance for that kind of behavior. Not that we cannot all expect people to perhaps feel a bit threatened in such precarious and uncharted emotional territory, but the minute the degrading language comes out about anyone I love . . . well that utterly changes the way I see the person speaking, and not for the better. Even if your SO can empathize with some of the emotional turmoil of an angry lover, IMHO he absolutely should insist that you be treated/discussed respectfully, like a human being equal in worth to him and anyone he dates.
Furthermore, if this lover needs to blow off some steam or just be frustrated and emotional for a minute in order to defuse herself . . . fine, she can go take it out on a punching bag, or rant for a minute to a friend who knows neither of the people in the relationship socially. By degrading you in front of your significant other, this lover is asking him to participate by overlooking that degrading language, and that's something that would end a relationship for me if it were not corrected. I will also add that if this woman is not only airing her frustrations with your SO, but with other mutual friends/acquaintances-- basically someone trying to socially shame you or make your life more difficult . . . then she really really must go. It was unclear whether this was the case for you, but In my experience, there is no way a relationship survives that intact.