In recent work, a statistical thermodynamic approach was used [J. Chem. Phys. 99, 7124 (1993)] to study curvature elastic properties of self-assembled films of nonionic surfactants at the oil/water interface in microemulsions. In the present work, this approach is extended to investigate films comprised of mixtures of ionic surfactants and nonionic cosurfactants, commonly used to form droplet and bicontinuous microemulsions. A simple description of the interactions among charged head groups is incorporated into the existing theoretical framework, yielding predictions of spontaneous curvature, mean and Gaussian elastic moduli, molecular area, and chain segment distributions as a function of monolayer composition, the strength of the electrostatic repulsion, and the lengths of the surfactant and cosurfactant chains. These predictions are found to be in good agreement with measured curvature elastic and structural properties, and with characteristic features of the phase diagrams of well-studied systems, particularly with respect to the effect of concentration of added electrolyte and the chain length and concentration of the alcohol (cosurfactant). More importantly, the results provide an unexpected explanation of the role of the alcohol in the stabilization of bicontinuous microemulsions, i.e., to form a monolayer of zero spontaneous curvature and low bending elastic moduli.