The authors solved a microscopic model that describes mixtures of a saturated phospholipid, an unsaturated phospholipid, and cholesterol. The method employed was the self-consistent field approximation. The model was capable of producing several classes of phase diagram, but only one of them showed a liquid-liquid coexistence region. The phospholipids in the cholesterol-rich liquid are more ordered than those in the cholesterol-poor liquid. Within this model, coexistence of two liquids in the ternary system is intimately tied to such coexistence in the binary cholesterolsaturated phospholipid system.