We use our quantum Gibbs ensemble Monte Carlo algorithm to perform computer experiments for the two-phase coexistence of a hydrogen-helium mixture. Our results are in quantitative agreement with the experimental results of Sneed, Streett, Sonntag, and Van Wylen. The difference between our results and the experimental ones is in all cases less than 15% relative to the experiment, reducing to less than 5% in the low helium concentration phase. At the gravitational inversion between the vapor and the liquid phase, at low temperatures and high pressures, the quantum effects become relevant. At extremely low temperature and pressure, the first component to show superfluidity is the helium in the vapor phase.