It would help to know how old you are, and how old he is.
Also, what kind of “bad things” did your parents find out in doing the background check? Is he divorced? Does he have children? All this would help to know.
Without knowing it, what I would suggest is asking your boyfriend about what you found out without letting him know how you found out. For instance, you can ask him broad questions about his background that would allow him, or give him the perfect opportunity to bring these past problems up. If he doesn’t, you can ask him specifically, if he has debt and how much.
At the end of the day you have to protect yourself and also be realistic. Some people have debt and that doesn’t mean that they’re bad boyfriends or potential husbands. So if you can be more specific, I can help you more clearly. 🙂