A family of chords will be the same, basically, in just about any musical situation. Built up off the basic notes of a particular scale. As in Cmaj. 3 majors, built on I, IV and V, three minors, built on ii, iii and vi, and one half diminished, built on vii.So these will be recognised as C, Dm, Em, F,G,Am and Bo in key Cmaj. The same concept applies in minor keys, not forgetting that three different sets of notes comprise these so there will be differing chords dependent on which set is being used. In jazz, melodic minor is the more usual.
That takes care of the triads. Jazzers like extensions, so as well as 1,3 and 5 making up a chord, 7,9,11 and 13 will be brought into use. They will still be 'rooted' in the originals, and often notes will be omitted. As in 13th - leave out 5, and maybe 9 and 11. Still recognisable as a 13th.
Altered notes are also de rigeur, as in #/b 5 and #/b9. Again these will use the basic triad as,- well,- a basis. Tritone substitution has been discussed on this site before, often with reference to the dominant chord.
So, the families are as ever, but with additions and changes to the same old relatives as before.