We present here the c-o colors for identified Flora, Vesta, Nysa-Polana, Themis, and Koronis family members within the historic data set (2015-2018) of the Asteroid Terrestrial-impact Last Alert System (ATLAS). The Themis and Koronis families are known to be relatively pure C- and S-type Bus-DeMeo taxonomic families, respectively, and the extracted color data from the ATLAS broadband c- and o-filters of these two families are used to demonstrate that the ATLAS c-o color is a sufficient parameter to distinguish between the C- and S-type taxonomies. The Vesta and Nysa-Polana families are known to display a mixture of taxonomies possibly due to Vesta's differentiated parent body origin and Nysa-Polana actually consisting of two nested families with differing taxonomies. Our data show that the Flora family also displays a large degree of taxonomic mixing and the data reveal a substantial H-magnitude dependence on color. We propose and exclude several interpretations for the observed taxonomic mix. Additionally, we extract rotation periods of all of the targets reported here and find good agreement with targets that have previously reported periods.