Caille analysis of the small-angle X-ray line shape of the lamellar phase of 7:3 wt/wt cetyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzene sulfonate (SDBS) bilayers shows that the bending elastic constant is kappa = (0.62 +/- 0.09)k(B)T. From this and previous results, the Gaussian curvature constant is kappa = (-0.9 +/-0.2)k(B)T. For 13:7 wt/wt CTAT/SDBS bilayers, the measured bending elasticity decreases with increasing water dilution, in good agreement with predictions based on renormalization theory, giving kappa(o) = 0.28k(B)T. These results show that surfactant mixing is sufficient to make K approximate to k(B)T, which promotes strong, Helfrich-type repulsion between bilayers that can dominate the van der Waals attraction. These are necessary conditions for spontaneous vesicles to be equilibrium structures. The measurements of the bending elasticity are confirmed by the transition of the lamellar phase of CTAT/SDBS from a turbid, viscoelastic gel to a translucent fluid as the water fraction is decreased below 40 wt %. Freeze-fracture electron microscopy shows that the gel is characterized by spherulite defects made possible by spontaneous bilayer curvature and low bending elasticity. This lamellar gel phase is common to a number of catanionic surfactant mixtures, suggesting that low bending elasticity and spontaneous curvature are typical of these mixtures that form spontaneous vesicles.