In order to explore the transport and coupling properties of multiferroic interfaces, a multiferroic/paramagnetic-composition thin film was investigated by successively growing La2/3Sr1/3MnO3 (LSMO) and BiFeO3 (BFO) multilayer-structure. Laser molecular beam epitaxy (LMBE) method was employed to prepare an idea structure of the composition thin film. Analysis of the leakage current demonstrates that the space-charge-limited current dominates the leakage current mechanism. Magnetic measurements show that the ferromagnetism of the composition thin film originates from BFO layer and the net magnetic moments could be responsible for the enhanced magnetoelectric coupling. The interface exhibits robust magnetodielectric effects at temperature points of 160K and 170K for zero field cooling (ZFC) and field cooling (FC), respectively. Furthermore, there exists a split in the loss tangent-temperature curves over temperature range of 150-170K between different cooling conditions, which is related to phase transition in the BFO layer.