A composite ab initio energy surface is obtained for the HeH2 triatomic molecular system by combining earlier calculations that covered parts of the surface. The extended surface covers the full angular range of He relative to the H-H axis as well as the full range of He-H-2 separations. As with all calculations thus far, the extended ab initio energy surface covers only a narrow range of H-H separations in the vicinity of 1.4 a.u., the equilibrium separation of ground state H-2. In addition, a new parametric representation of the ab initio energy surface is developed in terms of simple analytic functions based on the physics underlying the three principal interaction mechanisms responsible for the energy surface, and collisional applications are discussed briefly. All of the interaction mechanisms give rise to three-body interaction terms, an understanding of which is crucial to interpreting the behavior of the energy surface. This parametric representation reproduces the ab initio calculated values with an average [root-mean-square (rms)] percentage error under 7%, and because the parametric form is based on the physics, it can be extrapolated into the hitherto unexplored region of large H-H separations. A very interesting double inversion of the force between the two H atoms caused by proximity of He is explained. The H-H force is repulsive for large distances of He from H-2, weakly attractive for intermediate He distances, and strongly repulsive for small He distances.