Recent experimental investigations of the rotational motion of methane and molecular hydrogen using inelastic neutron scattering (INS) measurements in combination with thermodynamic techniques have provided a unique view of the evolution of the interaction of these two molecules with the MgO (100) surface and graphite basal plane. Despite significant differences in the chemical and physical properties and surface symmetry of these two adsorbents, the dynamical behavior of the adsorbed films is remarkably similar. The interaction of a CH4 monolayer solid with MgO and graphite, as monitored by the behavior of the J = 0 -> J = 1 free rotor transition, is so strong that there is no evidence for unhindered rotation of the molecule below 20 K. Using this same transition as a probe, H-2 monolayer solids exhibit nearly free or significantly hindered motion on graphite and MgO (100) surfaces, respectively. Investigations of CH4 and H-2 multilayer films on MgO find that once the film thickness exceeds similar to 3 layers, the molecule-molecule interactions predominantly determine the dynamical properties of the molecular film furthest from the surface. INS signals indicate that the dynamical motion in thicker films is closely related to that observed in the bulk system. The results of these studies serve as a valuable pathway for developing a qualitatively accurate description of the potential energy surfaces that govern the microscopic properties of these systems.