I feared that if I told him I lived with my parents he would quickly pick up on the fact that we don't have a healthy relationship,
If he picked up on you not having a healthy relationship, then its up to him to decide of you are a sweet, well adjusted person and just have some jerks in the family or he decides he doesn't want that dynamic. Its not where you come from, its what you do with it.
If you are ashamed that you live with your parents, then move.
But don't play it both ways -- tell your boyfriend how terrible your parents are and how abusive but then be doing nothing to change your dilemma by moving. He has proven that he doesn't have an unhealthy white knight complex and may have thought that is what you are fishing for. On the other hand, if you make the free choice of living with your folks, then don't share every single negative detail. make the best of it and don't use a boyfriend as a therapist.