Electrical control of magnetism is of great interest for low-energy-consumption spintronic applications. Due to the recent experimental breakthrough in two-dimensional materials, with the absence of hanging bonds on the surface and strong tolerance for lattice mismatch, heterogeneous integration of different two-dimensional materials provides a new opportunity for coupling between different physical properties. Here, we report the realization of nonvolatile magnetoelectric coupling in vdW sandwich heterostructure CuInP2S6/MnCl3/CuInP2S6. Using first-principles calculations, we reveal that when interfacing with ferroelectric CuInP2S6, the Dirac half-metallic state of monolayer MnCl3 will be destroyed. Moreover, depending on the electrically polarized direction of CuInP2S6, MnCl3 can be a half-metal or a ferromagnetic semiconductor. We unveil that the obtained ferromagnetic semiconductor in MnCl3 can be attributed to the different gain and loss of electrons on the two adjacent Mn atoms due to the sublattice symmetry broken by interlayer coupling. The effects of interfacial magnetoelectric coupling on magnetic anisotropy and ferromagnetic Curie temperature of MnCl3 are also investigated, and a multiferroic memory based on this model is designed. Our work not only provides a promising way to design nonvolatile electrical control of magnetism but also renders monolayer MnCl3 an appealing platform for developing low-dimensional memory devices.