The various bilayer structures formed from aqueous mixtures of an anionic (SDS) and a cationic surfactant (DTAB) with identical hydrocarbon C-12 chains at 40 degrees C have been investigated using small-angle neutron scattering (SANS) as well as static light scattering (SLS). The SANS data were analyzed using a paracrystal lamellar model with respect to the layer distance distribution and the number of layers in a single cluster. Unilamellar or oligolamellar vesicles form in the most diluted samples in the absence of added salt where the number of layers in a single cluster is found to be 1-3. Beyond the compositions where micelles form (30:70 < [SDS]:[DTAB] < 70:30), we observe a transition from vesicles to stacks of lamellar sheets upon increasing the overall surfactant concentration, indicated by an abrupt increase of the number of layers in a single cluster from 1-3 to infinity. Combined SANS and SLS data for samples containing vesicles ([SDS] + [DTAB] = 0.25 wt % in the absence of added salt) could be fitted with a model for unilamellar vesicles using a structure factor for sticky hard spheres, indicating that the vesicles attract each other and form clusters. However, at [SDS] + [DTPB] = 0.125 wt %, the vesicles appeared to be too large for the size distribution to he determined from our SANS and SLS data. in 0.1 M NaBr, the vesicles were clearly destabilized and either micelles or lamellar sheets form at most compositions and concentrations where vesicles predominate in the absence of added salt.