The best (not easy) way is to hang dry wall on resilient channels for the family room ceiling & insulate the joist cavity with fiber glass. I did this years ago in my previous home and it works well. You have to decouple the sound transmission path thru the joists to be effective and its best to eliminate any cutouts in the ceiling such as jucntion boxes. The fiberglass only controls the air transmission path. A suspended acoustic ceiling may help some but will not be as effective for the bass frequencies.
This approach also works with walls.
good luck!
This approach also works with walls.
good luck!