We present a framework for estimating exoplanet occurrence rates by synthesizing constraints from radial velocity and transit surveys simultaneously. We employ forward modeling with approximate Bayesian computation and mass-radius (M-R) relations of varying complexity to explore the population models describing these surveys, both separately and in a joint fit. Using this approach, we fit a joint power-law planet distribution function of the form d2 N/(dlogP dlogM) ~ Pb Ma, with a break in the power law in mass at Mb, to planets with orbital periods P = [25, 200] days and masses M = [2, 50] Mearth. We find that the M-R relation from Otegi et al. (2020), which splits rocky and volatile-rich planets into two populations that overlap in mass, allows us to find a model that is simultaneously consistent with both types of surveys. Our joint fit gives Mb = 21.6 (-3.2, +2.5) Mearth, nearly a factor of three higher than the mass break from transit-only considerations and an M-R relation without such an overlap. The corresponding break in the planet-star mass ratio of qb ~ 7×10-5 may be consistent with microlensing studies (qb ~ 6×10-5 - 2×10-4). Given that the microlensing detection method probes orbits far outside the Kepler parameter space, this finding indicates a similar most common mass both within and beyond the snow line. The joint fit also requires that a fraction of Frocky = 0.63 (-0.04, +0.04) planets in the overlap region belong to the rocky population. Our results strongly suggest that future M-R relations should account for a mixture of distinct types of planets in order to describe the observed planet population.