Be cautious with this one because your families interact so closely. It has a chance to become very awkward for everyone, particularly if he doesn't feel the same. If you wind up dating instead, your parents will likely provide more oversight as your families travel together.
Hopefully, you've been paying attention to whether your flirting is mutual. Watch his body language in particular. Try to get more alone time with him. See if the two of you can have a few "friend dates" doing something casual like going for ice cream or pizza and talking. Talk about both of your dating lives and compare what you're looking for in partners. If a dance or social event is coming up like a prom, see if he'll be your escort. Ask him for advice on how you find someone like him. This is your cue to describe what you like about him ("You're smart, have a good sense of humor, ... ."). Each step of the way, pay attention to his cues, both verbal and nonverbal.