Using integral equation theory of liquids to a binary mixed fluid lipid membrane, the authors study the membrane-mediated interactions between binding macroions and the redistribution of neutral and charged lipids due to the macroions. The authors find that when the concentration of binding macroions is infinitely dilute, the main contribution to the attractive potential between macroions is the line tension between neutral and charged lipids of the membrane. As the relative concentration of charged lipids is increased, the authors observe a repulsive-attractive-repulsive potential transition due to the competition between the line tension of mixed lipids and screened electrostatic macroion-macroion interactions. For the finite concentration of macroions, the main feature of the attraction is similar to the infinite-diluted case. However, the corresponding line tension of binary lipids under single macroion is lowered with the formation of multicomplexes by the charged lipids and the macroions, and the maximum of attractive potential will shift toward the higher values of charged lipid concentration.