Oh dear, this is a tricky one. The bottom line, is you aren't going to make everyone happy. It would be easy to say "tell your parents to mind their own business", but you live in their home.
The only solution I can think of is this. Sit down and have a real heart to heart talk with them both. Tell them that you love them and respect them and would never do anything to hurt them. However, you are an adult and them not trusting your choice of who to date hurts and insults you. Explain to them that they are going to have to try and trust you, as an adult, to make the right decisions for yourself. Otherwise, they are making you sad and feeling like they don't respect you as a person. Hopefully as, parents they will be able to see your point and that you are a good and trustworthy child of theirs that they can try to give a little space to. If not, then I'm not sure what to say. You can't let them control your life. Even if you are making a poor choice in boyfriend (I'm not saying you are), then you still have the right to go out and make those mistakes and learn from them, as you will at many times in your life. Your parents can't be there to shield you from everything.
If you speak to them respectfully and ask for some respect from them, maybe they will be able to come to some sort of an understanding.
Live as if you were to die tomorrow. Learn as if you were to live forever. - Mohandas Gandhi