The superlattice of energetically stable La2/3Sr1/3MnO3 and tetragonal BiFeO3 is investigated by means of density functional theory. The superlattice as a whole exhibits a half-metallic character, as is desired for spintronic devices. The interfacial electronic states and exchange coupling are analyzed in details. We demonstrate that the interfacial O atoms play a key role in controlling the coupling. The higher ferroelectricity of tetragonal BiFeO3 and stronger response to the magnetic moment in La2/3Sr1/3MnO3/BiFeO3 superlattice show a strongly enhanced electric control of the magnetism as compared to the rhombohedral one. Therefore, it is particularly practical interest in the magnetoelectric controlled spintronic devices.