In a recent paper [J. Chem. Phys. 2005, 122, 124318], a full-dimensional quantum method, designed to efficiently compute the rovibrational states of triatomic systems with long-range interactions, was applied to the benchmark Li-(H2) ion-molecule system. The method incorporates several key features in order to accurately represent the rovibrational Hamiltonian using only modestly sized basis sets: (1) exact analytical treatment of Coriolis coupling; (2) a single bend-angle basis for all rotational states; (3) phase space optimization of the vibrational basis; (4) G4 symmetry adaptation of the rovibrational basis. In this paper, the same methodology is applied for the first time to a van der Waals complex system, He(H2). As in the Li-(H2) study, all of the rovibrational bound states, and a number of resonance states, are computed to very high accuracy (1/10 000 of a wavenumber or better). Three different isotopologues are considered, all of which are found to have a single bound state with a very low binding energy. Several extremely long-lived Feshbach resonances are also reported.