The self-assembly in SOS-rich mixtures of the anionic surfactant sodium octyl sulfate (SOS) and the cationic surfactant hexadecyltrimethylammonium bromide (CTAB) has been investigated with the complementary techniques small-angle neutron scattering (SANS) and cryo-transmission electron microscopy (cryo-TEM). Both techniques confirm the simultaneous presence of open and closed bilayer structures in highly diluted samples as well as the existence of small globular and large elongated micelles at higher concentrations. However, the two techniques sometimes differ with respect to which type of aggregates is present in a particular sample. In particular, globular or wormlike micelles are sometimes observed with cryo-TEM in the vicinity of the micelle-to-bilayer transition, although only bilayers are present according to SANS and the samples appear bluish to the eye. A similar discrepancy has previously been reported but could not be satisfactorily rationalized. On the basis of our comparison between in situ (SANS) and ex situ (cryo-TEM) experimental techniques, we suggest that this discrepancy appears mainly as a result of the non-negligible amount of surfactant adsorbed at interfaces of the thin sample film created during the cryo-TEM specimen preparation. Moreover, from our detailed SANS data analysis, we are able to observe the unusually high amount of free surfactant monomers present in SOS-rich mixtures of SOS and CTAB, and the experimental results give excellent agreement with model calculations based on the Poisson-Boltzmann mean field theory. Our careful comparison between model calculations and experiments has enabled us to rationalize the dramatic microstructural transformations frequently observed upon simply diluting mixtures of an anionic and a cationic surfactant.