Gibbs-ensemble molecular simulations are reported for the vapour-liquid phase coexistence of a binary mixture characterised by an intermolecular potential which accounts for three-body interactions in addition to pairwise interactions. The simulations incorporate the influence of both three-body dispersion and three-body repulsion interactions. The effect of the non-additive Axilrod-Teller dispersion coefficient is investigated. It is concluded that the vapour-liquid coexistence of binary mixtures is unaffected by three-body interactions.