Small-angle X-ray (SAXS) scattering and N-14 NMR relaxation were determined for microemulsion samples formed from didodecyl dimethylammonium bromide (DDAB), water, and tetradecane to deduce the associated microstructures. The swelling features within the tetradecane microemulsion are unusual compared with those of DDAB/water/alkane analogues formed with shorter n-alkanes: tetradecane-containing microemulsions do not show the characteristic anti-percolation transition seen for the latter microemulsions. Experimental data along tetradecane dilution lines are consistent with a continuous transition from a bilayer to monolayer structure of the surfactant interface. The evolution is topologically complex. It involves the annealing of bilayer punctures that occur on oil dilution. A quantitative model that allows continuous transformation from multihandled bilayers (typical of L-3 sponge mesophases) to multihandled monolayers (typical of microemulsions modeled with shorter chained alkanes) is proposed that well fits the observed behavior.