We predict that the tunneling electroresistance effect is present at finite bias even in multiferroic tunnel junctions (MFTJs) with inversion symmetry. The effect is highly sensitive to the relative magnetization orientation in the electrodes. In addition, we demonstrate control of the bias-dependence of the tunneling magnetoresistance (TMR) in MFTJs via switching of the ferroelectric polarization of the barrier. The polarization induces a monotonic bias behavior in TMR which can be reversed by polarization switching. The magnitude of both effects is proportional to the polarization. The underlying mechanism is the inversion symmetry breaking due to the polarization combined with the interplay of the bias-induced and polarization-induced spin-dependent interfacial screening. These results expand the possibilities for the next-generation multifunctional devices.