Vesicle and micellar structures formed by mixtures of the oppositely charged surfactants cetyltrimethylammonium bromide (CTAB) and sodium octyl sulfate (SOS) with and without added sodium bromide (NaBr) have been examined by small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) techniques. The resulting spectra have been evaluated using a Fourier transform/deconvolution technique. Through indirect Fourier transformation of the scattering intensity and subsequent deconvolution of the resulting cross-sectional pair distance distribution function, detailed information of the cross-sectional and interfacial dimensions of the aggregates is obtained. SANS and SAXS show that the vesicle bilayer has a core radius of 9 Angstrom and a headgroup region extending an average 9 Angstrom more. SANS results for the micelles investigated indicate a core radius of 10-11 Angstrom and a headgroup region of 10 Angstrom. This analysis, when compared with theoretical calculations from a thermodynamic cell model, indicates that the surfactant headgroups occupy a diffuse region near the core/water interface.