If your family aren't hard-core musical fans, then I'd think that they will definately enjoy it.
It is one of my favorite musicals, and it got me started with this musical craze, but I now think it's not that great... I mean I'm sure non-musical people who thinks they've seen lots of different shows that they think they know everything/people who are totally new to the world of musicals, might say this is the best show on the planet. I, however, don't think it's that good. There's a lot of talent, but everything (story, music, cast, choreography, etc) just doens't blend in together in my opinion.
"Hey, you! You're the worst thing to happen to musical theatre since Andrew Lloyd Webber!"
-Family Guy