Buoyancy-Marangoni convection in a cavity with side heating has been studied analytically and numerically in superposed immiscible liquid layers with a free surface. The analytical results (based on an assumption of infinite aspect ratio) indicate that four different flow patterns are possible and that these results may be anticipated on the basis of the introduction of a new parameter which represents the combined effects of Marangoni forces acting at the interface between the two liquids and at the free surface. It is shown further that the new parameter is a unique thermocapillary quantity which influences the convection in the lower layer. For finite cavities, some numerical results on the mutual influence of the two layers have been presented. The numerical results obtained near the centre of the cavity are in good agreement with the results from the analytical model for sufficiently large aspect ratios.