Owing to small critical thickness and high lattice matching with typical ferromagnetic metal electrodes, barium titanate is often employed as the tunneling layer of multiferroic tunnel junctions, and barium titanate-based multiferroic tunnel junctions are considered to possess significant application potential in the field of non-volatile memory. It was found experimentally that the tunneling magnetoresistance (TMR) of barium titanate-based multiferroic tunnel junctions does not monotonically vary with the bias voltage. The physical mechanism of the above phenomenon needs to be clarified theoretically. On the other hand, the interplay between the ferromagnetic effect and the ferroelectric effect in the barium titanate-based multiferroic tunnel junction needs to be investigated systematically. In this paper, we have calculated the tunneling magnetoresistance and the tunneling electroresistance of Co/BTO/LSMO multiferroic tunnel junctions by using the Airy function, and systematically study the influences of bias voltage and the thickness of tunneling layer. The results show that there exist oscillations in the curves of the TMR and tunneling electroresistance (TER) versus both bias voltage or the thickness of tunneling layer. Physically, the oscillations originate from the quantum interference effect in the tunneling process. In addition, the tunneling magnetoresistance effect in Co/BTO/LSMO multiferroic tunnel junction is quite weak, which arises from the influence of the polarization on the potential structure of the tunneling layer. This will lead that the magnetic arrangement of ferromagnetic electrode has little influence on the tunneling electroresistance effect, which agrees with the experiments. It indicates that the traditional barium titanate-based multiferroic tunnel junctions are unfavorable to serve as four-resistance state devices in the field of memory.