Saturated phospholipids, unsaturated phospholipids, and cholesterol are essential components of cell membranes, making the understanding of their mutual interactions of great significance. We have performed microsecond molecular dynamics simulations on the ternary mixtures of DPPC/POPC/cholesterol to systematically examine lipid-lipid and cholesterol-lipid interactions in the liquid-ordered and the liquid-disordered phases. The results show that there exists a competition between the tighter packing of cholesterol-lipid and the looser packing of lipid-lipid as the membrane changes from the liquid-disordered phase to the liquid-ordered phase. Depending on the lipid saturation, the favor of lipid-lipid interactions is in the order of saturated-saturated > monounsaturated-monounsaturated > saturated-monounsaturated. Cholesterol-saturated lipid interactions are more favorable than cholesterol-monounsaturated lipid ones. The results are consistent with the push-pull forces derived from experiments and give general insights into the interactions among membrane components.