Volumetric properties of liquid mixtures of neon and hydrogen have been calculated using path integral hybrid Monte Carlo simulations. Realistic potentials have been used for the three interactions involved. Molar volumes and excess volumes of these mixtures have been evaluated for various compositions at 29 and 31.14 K, and 30 atm. Significant quantum effects are observed in molar volumes. Quantum simulations agree well with experimental molar volumes. Calculated excess volumes agree qualitatively with experimental values. However, contrary to the existing understanding that large positive deviations from ideal mixtures are caused due to quantum effects in Ne-H-2 mixtures, both classical as well as quantum simulations predict the large positive deviations from ideal mixtures. Further investigations using two other Ne-H-2 potentials of Lennard-Jones (LJ) type show that excess volumes are very sensitive to the cross-interaction potential. We conclude that the cross-interaction potential employed in our simulations is accurate for volumetric properties. This potential is more repulsive compared to the two LJ potentials tested, which have been obtained by two different combining rules. This repulsion and a comparatively lower potential well depth can explain the positive deviations from ideal mixing.