Using high spatial resolution HST WFC3 and ACS imaging of resolved stellar populations, we constrain the contribution of thermally-pulsing asymptotic giant branch (TP-AGB) stars and red helium burning (RHeB) stars to the 1.6 um near-infrared (NIR) luminosities of 23 nearby galaxies. The TP-AGB phase contributes as much as 17% of the integrated F160W flux, even when the red giant branch is well populated. The RHeB population contribution can match or even exceed the TP-AGB contribution, providing as much as 21% of the integrated F160W light. The NIR mass-to-light (M/L) ratio should therefore be expected to vary significantly due to fluctuations in the star formation rate over timescales from 25 Myr to several Gyr. We compare our observational results to predictions based on optically derived star formation histories and stellar population synthesis (SPS) models, including models based on the Padova isochrones (used in popular SPS programs). The SPS models generally reproduce the expected numbers of TP-AGB stars in the sample. The same SPS models, however, give a larger discrepancy in the F160W flux contribution from the TP-AGB stars, over-predicting the flux by a weighted mean factor of 2.3 +/-0.8. This larger offset is driven by the prediction of modest numbers of high luminosity TP-AGB stars at young (<300 Myrs) ages. The best-fit SPS models simultaneously tend to under-predict the numbers and fluxes of stars on the RHeB sequence, typically by a factor of 2.0+/-0.6 for galaxies with significant numbers of RHeBs. Coincidentally, over-prediction of the TP-AGB and under-prediction of the RHeBs result in a NIR M/L ratio largely unchanged for a rapid star formation rate. However, the NIR-to-optical flux ratio of galaxies could be significantly smaller than AGB-rich models would predict, an outcome that has been observed in some intermediate redshift post-starburst galaxies. (Abridged)