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This paper presents a model for two-phase nanofluid-fluid flow and heat transfer. The nonuniform nanoparticles are transported using Buongiorno model by convection, Brownian diffusion and thermophoresis. This is the first attempt to employ Buongiorno model for two-phase nanofluid-fluid flow. The moving interface between the nanofluid and the immiscible fluid is captured using the level-set method. The model is first verified and then demonstrated for coupled flow and heat transfer in (1) a water–alumina nanofluid-filled cavity with a rising silicone oil drop and (2) stratified flow of water–alumina nanofluid, pure water and silicone oil in a channel.