The water-in-oil (w/o) microemulsion regions formed by the double-chained DDAB surfactants with the two aromatic oils toluene and trifluoromethylbenzene have been investigated with the highlight on the microstructural features. A remarkable finding is that DDAB is soluble up to similar to 30 wt % in these oils. The phase diagrams of DDAB/water/aromatic oil systems show a microemulsion region near the oil-DDAB axis, with a maximum water uptake of similar to 15 wt %. Along the oil dilution line, the water/surfactant (w/s) mass ratio is 0.16; at high surfactant concentrations, the lamellar region is seen to melt gradually into the isotropic microemulsion through a very small two-phase region. N-14 NMR relaxation times and conductivity measurements, collected along water and oil dilution lines, have suggested the existence of flexible bilayers at high volume fractions of the dispersed phase (phi(d)), whereas at low phi(d), self-association of the oil highly perturbs the expected w/o organization of DDAB molecules, which become almost molecularly dispersed. The interpretation of the slow N-14 NMR correlation times in terms of the percolation theory gives critical exponents in agreement with a dynamic regime at intermediate phi(d) and with a static regime at high phi(d) in the proximity of the lamellar phase.