We present a new method for measuring the photometry of objects around galaxy clusters, employing a novel mode-filtering technique for both detection and photometry. With this, we are able to investigate the galaxy populations inside the 25 massive clusters observed by the Cluster Lensing and Supernova survey with Hubble (CLASH). We produce multi-wavelength catalogs covering 16 bandpasses from ultraviolet (∼2360 Å) to infrared ($\sim 1.54 $) including photometric redshifts. A comparison with spectroscopic values from the literature finds that ∼82% of our reported photometric redshifts lie within |zp − zs|/(1 + zs)<0.05. This improvement in redshift accuracy, in combination with a detection scheme designed to maximize purity, yields a substantial upgrade in cluster member identification over the previous CLASH galaxy catalog. We find consistency between the galaxy magnitudes, colors, and photometric redshifts obtained here and from previous studies, including a deeper observation of one of the CLASH clusters. Evaluating the luminosity functions for these clusters, we find that we are able to observe galaxies down to ${\rm M} \sim {\rm M}^* + 5$, and the values of M* we derive are consistent with that expected from published cluster galaxy luminosity functions. These clusters follow a consistent trend in mass-richness that agrees with low-mass cluster observations. We measure luminosity functions for these clusters, which we use to derive total luminosity, and, from that, stellar masses. We find stellar mass fractions of 1.8 ± 0.7% of the total halo mass, in agreement with previous studies. Not only will this catalog enable new studies of the properties of CLASH clusters, but the photometric techniques we use set the stage for future surveys of galaxy clusters.