Bending elasticity moduli of equilibrium bilayers and monolayers of surfactants are calculated using a previously developed self-consistent field lattice model. The model is extended by incorporating ionic interactions at curved interfaces, so that ionic surfactants can be treated as well. The interfaces are formed by self-assembling of the surfactants. It is found that the size of the counterions is an important parameter in determining the bending moduli of charged interfaces. Screening the electric double layer by salt has two opposing effects on the rigidity of monolayers and bilayers of ionic surfactants. The first is that suppression of the double layer as such would make the layers less rigid. However, this trend is outweighed by the simultaneously occurring thickness growth. The sum effect is therefore that the surfactant layers are more rigid in higher salt concentrations. In the case that salt ions decrease the solvent quality, as salting-out ions do, the rigidity of the layer passes through a maximum in high salt concentrations (ca. 1 kmol/m3). The spontaneous curvature of a water-dodecane-sodium dodecyl sulfate system depends on the ionic strength in solution. We predict that the preferential curvature changes sign twice when the ionic strength increases. This can be explained by a continuous increase in packing density of the surfactant layer upon an increase in ionic strength. There are at least two factors contributing to the observed behavior : (1) The shape of the surfactant becomes increasingly important when packing density increases. (2) The difference in the ability of the solvents (dodecane and water) to penetrate into the surfactant layer becomes, especially at high packing densities, a curvature determining factor.