I have a situation like this at the moment, but, like the person a few above, I'm good friends with a boy who has a girlfriend.
His girlfriend seems very different to you, mind, but she's made me feel very uncomfortable by accusing me of acting guilty around her, telling my other friends that she has a problem with me and being openly resentful of any time that me and her boyfriend spend together, even though we share 3 classes, have similar career interests and go to many of the same extra-curricular activities. I am confident that I have done nothing to indicate that I am interested in a closer relationship with him.
It hasn't really been resolved as of yet, I have just learnt to let them have as much space as his girlfriend needs, which isn't an ideal situation.
What might be helpful to you, is that I would hate for him and his girlfriend to split up, they've been together for a long time and are in love - as much as she seems to dislike me, I like to see them together. So if this is the only problem in your relationship then I don't think you should end it, but do what you think is best because no-one on here knows the full situation except you.