Mixtures of the oppositely charged surfactants cetyltrimethylammonium bromide (CTAB) and sodium octylsulfate (SOS) combine to form an array of microstructures at various mixing ratios. At certain compositions, thermodynamically stable unilamellar vesicles form. To determine the composition of these vesicles, we have performed small-angel neutron scattering (SANS) experiments, using a contrast variation technique, on samples containing 2.0 wt % 3/7 (weight ratio) CTAB/SOS, which is a bulk composition of 21 mol % CTAB. The scattering contrast between the aggregates and the solvent was varied internally by substituting varying amounts of the SOS with deuterated SOS. Using a modified Guinier analysis of the data, we infer a vesicle composition that is 45 mol % CTAB, which is much more nearly equimolar than the bulk mixing ratio, and we find a bilayer thickness of 22 Angstrom. In parallel to the SANS experiments, we have developed a thermodynamic cell model to predict microstructure properties. The model results for composition and bilayer thickness compare very well with SANS results. When sodium bromide (NaBr) is added to solutions at these bulk compositions, a transition to micelles occurs, and samples transform from bluish to clear. SANS experiments with samples containing 5.0 wt % (0.5 M) NaBr yield the expected result that the micelles have a composition equal to that of the bulk and are ellipsoidal or cylindrical in shape. Thus, the addition of NaBr at this surfactant concentration favors the formation of increasingly charged microstructure, and simple packing arguments suggest that the resulting increase in head-group electrostatic repulsions favors a smaller, more highly curved microstructure, i.e., micelles, over a flatter bilayer vesicle phase.