The HMSA integral equation has been solved for the binary mixture He-H 2 over a range of densities and compositions at 100 K and 300 K. Comparison of the radial distribution functions and the pressures shows that these results are in good agreement with those of two-component MC simulations close to the binodal curve or melting line. The HMSA equation of state rather than the usual van de Waals one fluid approximation was used to calculate the Gibbs free enthalpy; the latter was used to determine the fluid-fluid phase separation in the mixture. The spinodal curve calculated from the composition fluctuation structure factor SCC(k), is not consistent with the binodal curve, probably due to inconsistencies in this structure factor. The direct correlation functions that result from the integral equations were used to calculate the freezing of the mixture with the Haymet and Oxtoby version of density functional theory of freezing, where the grand potential of the solid is expanded up to second order. To force quantitative agreement with experimental results, the fourth star was omitted from the HCP reciprocal lattice. An important result is the solubility of helium in the hydrogen-rich solid of a few mole percent. The authors also find the interesting phenomenon of density inversion between the hydrogen-rich solid and the hydrogen-rich fluid.