The flexible surface model is a powerful framework in which to describe the thermodynamics of fluid. membrane phases. In the case of balanced microemulsions (and their bilayer analogue, the L(3) phase), a general form for the free energy density has been proposed. In this paper, we consider the phase behavior of balanced microemulsions and show that this model is successful in capturing the important features of experimentally determined phase diagrams of systems which exhibit this remarkable phase.