I'm very sorry this happens to you.
It's not clear from your question exactly what you are saying when you respond to them, but one approach that I read about once somewhere and really liked is this: when someone does something you find hurtful, say, very calmly and straightforwardly, "I feel demeaned" or "I feel mocked" or "I feel hurt" and possibly, "Please stop".
There are two keys to this:
(1) It is important that you try to focus on only talking about how you feel and limit as much as possible what claims you make about them. When it comes to how you feel, they can't really tell you you're wrong without sounding absurd. Who can disagree with a person who makes a statement like "I feel demeaned"? Only you know how you feel and that is obvious. On the other hand, if you say something like, "you're being hurtful," they can argue that you just misinterpreted them. If you try to argue about the particulars of what they are saying, they can easily disagree and say you're wrong, and a fight will ensue.
(2) Stay calm so as to appear to be the most rational one. If they try to tell you to lighten up or get mad at you for not taking a joke, just stay calm and stick with your story, "I feel demeaned and I would like it if you would stop". Don't lash out. If you become angry or upset, or try to insult them in defense, they will get defensive and angry in return, and a fight will ensue.
By sticking strictly to only speaking about your own feelings and remaining calm, the hope is that this will ultimately make them feel embarrassed by their behavior and they will stop in order to stop feeling embarrassed. I've tried this on acquaintances who are often hurtful and they have stopped and apologized (and are overall less mean since then), so it seems effective.
Lastly, here is an article series about how not to get your buttons pushed: http://www.psychologytoday.com/blog/evolution-the-self/200910/disarming-your-buttons-how-not-get-provoked-part-3-4 It's not the article I mentioned above, because I can't find that one. I think I found it when searching for phrases like "how to deal with invalidation" and "how to set boundaries" so maybe you will stumble across it too. Good luck!
EDIT: I just realized I didn't really answer the question. It's very hard to say why they do this without knowing more about your parents and your history. There could be many reasons: they feel threatened by you, they think they are just having fun, they are trying to force you to be a certain way (e.g., more self-deprecating), etc. Perhaps you should talk to a family therapist about this.