The phase behavior of the ternary monoolein (MO)-diolein (DO)-water ((H2O)-H-2) system is presented. The experimental phase behavior and microstructure are studied by a combination of polarizing microscopy, small-angle X-ray diffraction, and NMR methods. Monoolein forms extensive reversed bicontinuous cubic liquid crystalline phases (C) that are in equilibrium with a lamellar liquid crystalline phase (L-alpha) on the water-poor side and with excess water on the other side. The presence of small amounts of DO in the MO-water system is sufficient to destabilize the C and L-alpha liquid crystalline phases. Formation of a reversed hexagonal (HII) phase from the cubic phase occurs at a lower transition temperature than that reported for the MO-water system. Within the cubic region, the diamond cubic phase, CD, is less stable than the gyroid type, C-G. The solubility of DO increases within this phase when the MO content increases, and the phase reaches its maximum stability at 4 wt % DO. The large HII-phase formed in the ternary system is in equilibrium with water, and it solubilizes about 30 wt % DO within its stability range. A stable dispersion is formed at even higher DO concentrations. An ideal swelling of the HII-phase with increasing polar volume fraction is observed, whereas the length of the hydrocarbon chains along the hexagonal faces is constant. We measure a slight change of the average area per molecule in the H-II-phase with DO concentration. The formation and stability of the liquid crystalline phases can be qualitatively understood from the self-aggregation model, using the geometrical packing parameter of the lipids.