Here's that question

Well that's very linguine !! Well it would really help here if we knew which gender box you fell into, but I'd say have a little blow up at them using sentences like " private & embarrassing like the time I saw you two..... (make something up), and did you notice I didn't go around making fun" !!..
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No one should be throwing stones in a glass house...
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This too will pass...
C...

Eeek!..One time my parents heard me having phone sex, totally humiliating...
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Anyway, can you tell your dad to quit it with the jokes?..Maybe just say "look, that was really embarrassing for me, and I'd appreciated it if you stopped."..Or you could give it right back to him, like, "Yeah, I'm glad I"m not married like you, otherwise I'd probably have to do it in the bathroom when mom's not home."..(Or something more witty than that.)..
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This might be one of those things that time just has to make people forget about...And it WILL fade...In the meantime, at least be thankful that your parents seem to think it's funny, and aren't being all awkward and stiff around you...That's the worst...

Move out? ..
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Holy cannoli, that is embarrassing. You can't see it through the computer screen, but my face is actually becoming flushed, just reading your question. Oh my...
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OK, let's see here. Honestly, what are your options? You could talk to your parents about it (eep!) or you could take the high road and ignore your dad's jokes. Just like the kids who used to tease you in eighth grade, sooner or later he'll grow weary of joking when he is no longer getting a reaction. One hopes. ..
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Or you could just move out...

this isn't an answer to "what should I do"?, but it's an attempt to answer Carlos' question: I think the person asking this question is female. ..
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For some reason I can't imagine a guy saying "I am mortified." ..
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that's all...

if your dad is being THAT much of a jerk about it, start making vulgar comments about what you were caught doing, so he will be so uncomfortable that he just won't bring it up anymore... like if you're a guy just say "yeah, i was really crankin' it...if you had walked in 2 minutes later i probably would have shot you in the eye."..or if you're a girl... well i dunno...then your dad shouldn't be talking about that with you...ewww!..maybe you could be like "well i got some deep dicking earlier but i still had to come home and finish myself off."..that's what i would do, but i'm kind of a bitch...i dunno... but he's just being rude...