The 2011 paper How Many Species Are There on Earth and in the Ocean? indirectly answers this question as well as any other source you'll find I imagine. It estimates how many species there are total based on the rate of discovery of higher taxa; it includes plots of number of taxa over time for the major groups of life in Figure S1. Which gives:
Animalia - 5300 families in 2011 (the plots are given with only one significant figure, the second one's my estimate) (estimated total: 5800)
Chromista - 270 families (estimated total: 360)
Fungi - 550 families (estimated total: 620)
Plantae - 750 families (estimated total: 800)
Protozoa - 280 families (estimated total: 310)
Archaea - 27 families (no estimated total; the number has been increasing exponentially so far)
Bacteria - 300 families (same as for Archaea)
Which gives us a total of 7477 families in 2011, with an estimated total of (ignoring Archaea and Bacteria, who don't really fall in the same kind of classification anyway) 7890 families. (make that 7500 families discovered by 2011 and 8000 estimated in total given the imprecision involved in my reading the plots).