We present a homogeneous analysis of line and continuum emission from simultaneous high-cadence spectra and photometry covering near-ultraviolet and optical wavelengths for 20 M dwarf flares. These data were obtained to study the white-light continuum components at bluer and redder wavelengths than the Balmer jump. Our goals were to break the degeneracy between emission mechanisms that have been fit to broadband colors of flares and to provide constraints for radiative-hydrodynamic (RHD) flare models that seek to reproduce the white-light flare emission. New model constraints are presented for the time evolution among the hydrogen Balmer lines and between CaII K and the blackbody continuum emission. We calculate Balmer jump flux ratios and compare to the solar-type flare heating predictions from RHD models. The model ratios are too large and the blue-optical ({lambda}=4000-4800{AA}) slopes are too red in both the impulsive and gradual decay phases of all 20 flares. This discrepancy implies that further work is needed to understand the heating at high column mass during dMe flares.