A new highly accurate interaction potential is constructed for the He-H2 van der Waals complex. This potential is fitted to 1900 ab initio energies computed at the very large-basis coupled-cluster level and augmented by corrections for higher-order excitations (up to full configuration interaction level) and the diagonal Born-Oppenheimer correction. At the vibrationally averaged H-H bond length of 1.448736 bohrs, the well depth of our potential, 15.870 ± 0.065 K, is nearly 1 K larger than the most accurate previous studies have indicated. In addition to constructing our own three-dimensional potential in the van der Waals region, we present a reparameterization of the Boothroyd-Martin-Peterson potential surface [A. I. Boothroyd, P. G. Martin, and M. R. Peterson, J. Chem. Phys. 119, 3187 (2003)] that is suitable for all configurations of the triatomic system. Finally, we use the newly developed potentials to compute the properties of the lone bound states of (4)He-H2 and (3)He-H2 and the interaction second virial coefficient of the hydrogen-helium mixture.