To understand Microwave (MW) heating and boiling of binary liquid mixtures, a new multiphysics model was developed. The new model solves Maxwell's equations for the electromagnetic field distribution. Concerning the coupled dispersed and segregated vapor-liquid flow during MW boiling, it was modelled based on a hybrid Two-Fluid-Volume-of-Fluid method. As for the modelling of heat and mass transfer, Two-fluid energy and species conservation equations were solved, with new dispersed and segregated interphase heat and mass transfer closures formulated using appropriate interface jump conditions combined with vapor-liquid equilibrium relations. The new model showed reasonably good agreement with the experimental data. The capability of the model to simulate MW heating, superheating, superboiling, and interphase transfer phenomena in methanol-water mixture (heated in a multi-mode MW cavity) was demonstrated, and the associated physics was investigated. The simulation results revealed three underlying mechanisms that lead to superheating (up to 9.5° C at 300 W) in binary mixtures, namely limited bubble nucleation, inefficient mixing, and higher interfacial saturation temperature compared to that in bulk liquid (about 2° C higher). Besides, the results also showed that the increase of heating time mainly increases the amount of superheat rather than the superheat temperature. It was also found that MW superheating tends to reduce the mass fraction of the lighter component in the released vapor (by up to 2%). In the subsequent study, the effects of several operating conditions were examined. The simulation results generally showed that higher liquid methanol concentration, higher MW power, rectangular sample geometry, and smaller sample volume lead to higher superheat intensity, but poorer methanol concentration in the vapor released. The new model and findings could open up new avenues for the design and improvement of processes such as MW-assisted synthesis, extraction, biodiesel production, and distillation.