A new model of two-phase thermocapillary-buoyancy convection with phase change at gas-liquid interface in an enclosed cavity subjected to a horizontal temperature gradient is proposed, rather than the previous one-sided model without phase change. We study the onset of multicellular convection and two modes of convective instability, and find four different flow regimes. Their transition map is compared with the non-phase-change condition. Our numerical results show the stabilizing effect of interfacial phase change on the thermocapillary-buoyancy convection.