I agree with Bryce556 - you can lie without actually lying, just only give them the information you know they will accept
Or you can just tell them that you are going out with/sleeping at some guy friend, I did that myself sometimes in my first realtionships (not that my parents were strict about this, they are more liberal than I could wish for, but I would get just too embarased to say I was going out with a girl at that time

).
One last thing you can try is just asking them to talk about it with you and convicing them to give you some more freedom, agreeing on some "rules" if needed. I think it should work if they are able to think at least a bit reasonably and your family is not very religious, traditional or something like that (no sex before marriage and blahblahblah). Might be good to try and talk to your father first, I guess he had such problems too when we was young so he could understand you easier and help you in a later argument with your mom. Good luck
