Equimolar mixtures of dodecyltrimethylammonium chloride (DTAC) and sodium octyl sulfonate (SOSO) show a vesicle phase at > 99 wt % water and a single, fluid lamellar phase for water fractions below 80 wt %. This combination is consistent with the bilayer bending elasticity kappa approximate to k(B)T and zero bilayer spontaneous curvature. Caille line shape analysis of the small-angle X-ray scattering from the lamellar phase shows that the effective K depends on the lamellar d spacing consistent with a logarithmic renormalization of kappa with kappa(o) = (0.8 +/- 0.1)k(B)T. The vesicle size distribution determined by cryogenic transmission electron microscopy is well fit by models with zero spontaneous curvature to give (kappa + (kappa/2)) = (1.7 +/-0.1)k(B)T, resulting in kappa = (1.8 +/- 0.2)k(B)T. The positive value of kappa and the lack of spontaneous curvature act to eliminate the spherulite defects found in the lamellar gel phases found in other catanionic mixtures. Current theories of spontaneous bilayer curvature require an excess of one or more components on opposite sides of the bilayer; the absence of such an excess at equimolar surfactant ratios explains the zero spontaneous curvature.