We present a new gravitational lens model of the Hubble Frontier Fields cluster Abell 370 (z=0.375) using imaging and spectroscopy from Hubble Space Telescope and ground-based spectroscopy. We combine constraints from a catalog of 909 weakly lensed galaxies and 39 multiply imaged sources comprised of 114 multiple images, including a system of multiply imaged candidates at z=7.84+/-0.02, to obtain a best-fit mass distribution using the cluster lens modeling code strong and weak lensing united. As the only analysis of A370 using strong and weak lensing constraints from Hubble Frontier Fields (HFF) data, our method provides an independent check of assumptions on the mass distribution used in other methods. Convergence, shear, and magnification maps are made publicly available through the HFF website (http://www.stsci.edu/hst/campaigns/frontier-fields). We find that the model we produce is similar to models produced by other groups, with some exceptions due to the differences in lensing code methodology. In an effort to study how our total projected mass distribution traces light, we measure the stellar mass density distribution using Spitzer/Infrared array camera imaging. Comparing our total mass density to our stellar mass density in a radius of 0.3Mpc, we find a mean projected stellar to total mass ratio of <f*>=0.011+/-0.003 (stat.) using the diet Salpeter initial mass function. This value is in general agreement with independent measurements of <f*> in clusters of similar total mass and redshift.