Historically, the simulation of phase equilibria has focused largely on the use of effective intermolecular potentials such as the Lennard-Jones potential. Although the use of such potentials has proved useful in obtaining good agreement with experimental properties, they inhibit the investigation of the separate roles of two, three and higher body interactions. Our previous work on three-body interactions indicated that such interactions are important in accurately determining the vapour-liquid phase envelope of pure fluids. However, their effect on the vapour-liquid equilibria of binary mixtures and solid-liquid equilibria remained largely unknown. In this work, we report molecular simulation calculations that involve true two-body and three-body intermolecular potentials for both binary mixtures and solid-liquid equilibria. We demonstrate that three-body interactions are more important that previously belived. Comparison with experiment indicates that accounting for three-body interactions can considerably improve the prediction of both binary mixture phase equilibria and solid-liquid phase equilibria.