The correspondence between the equilibrium phase behavior of oil-water-surfactant mixtures and the macroemulsion type and stability is examined. Both the phase behavior and emulsion stability are argued to be dependent on the bending elasticity of the surfactant monolayer at the oil-water interface. At positive spontaneous curvatures, O/W emulsions are stable; at negative spontaneous curvatures W/O emulsions are stable, whereas, in the balanced state of the surfactant film, an emulsion break usually occurs for a wide variety of systems. To explain the effect of the monolayer bending properties on the macroemulsion stability, the thermally activated rupture of emulsion films is theoretically studied. We consider emulsion films covered by saturated surfactant monolayers, with strong lateral interactions among the adsorbed surfactant molecules. The monolayer at the edge of a nucleation hole in the emulsion film is strongly curved; the bending energy penalty involved leads to a strong dependence of the coalescence barrier on the sign and the absolute value of the monolayer spontaneous curvature. By contrast with earlier hole nucleation theories, the emulsion film thickness is allowed to vary, in order to minimize the free energy of the nucleation hole. At large positive spontaneous curvatures, Ho, the oil-water-oil (O/W/O) films are stable, with a coalescence barrier, in a first approximation, proportional to the bending modulus kappa. On the other hand, W/O/W films break without a barrier. Conversely, for large negative values of Ho, W/O/W films are stable, while O/W/O films break without a barrier. In the vicinity of the balanced state, a very steep change in film stability with Ho is predicted. The model reproduces the macroemulsion stability sequence : O/W emulsion-emulsion breakage-W/O emulsion, observed in polyethoxylated nonionic surfactant-oil-water mixtures with increasing temperature. The macroemulsion break is predicted to occur at the balanced (PIT) point, as has been observed experimentally by Shinoda et al. The hole nucleation in multilamellar-stabilized films is shown to be drastically suppressed, in agreement with the experimental findings of Friberg et al. For rigid surfactant monolayers (kappa similar to 100 kT) and multilamellar-stabilized systems, a region of stable multiple emulsions is predicted, while it is prohibited for flexible (kappa similar to 1 kT) monolayers. Possible extensions of the model to other systems are discussed.