The interlayer proximity effect induced by spin-orbital coupling between the monolayers of borophosphene (BP) and MoSe2 in the stacked heterostructure is studied by first principles calculations. The proximity effect originates from the hybridization of the d orbital of the Mo atoms and the p orbital of the B atoms. This hybridization greatly improved the strength of spin-orbital coupling of the BP layer, bringing the spin-dependent valley and spin splitting about 13 meV at the K point of the conduction band of BP layer. Moreover, the existence of BP layer destroyed the mirror symmetry of MoSe2 layer, causing the Rashba splitting at the Γ point of the valence band. In addition, the calculation results indicate that both the Zeeman splitting and Rashba splitting can be modulated by the transverse electric field and the interlayer distance.