Technically speaking a family of musicians is a family, in which at least two members of a different generation make music. So, this is father and son, mother and daughter and so on. I wouldn't consider a family in which two brothers or three brothers make music a family of musicians. But you could, it's okay with me. The Jackson Five are actually no family of musicians, not in the sense of the Bachs from Thuringia. But, we don't want to be too hard and because they are soooooooooo famous, here and no and for us they are a family of musicians. The Kelly Family however, with their singing dad, match the criteria easily.
Those who want to learn more about the most famous families of musicians in the world and in the past three hundred years, just click yourself away from here. But don't be disappointed: there haven't been really many famous families of musicians on earth and there weren't really big ones. One exception.