Spin-dependent electronic transport through multiferroic Co/PbTiO₃/Co tunnel junctions is studied theoretically in view of the recent observation of an inverse TMR in Co/PbTiO₃/LaSrMnO₃ heterostructures. Conductances calculated within the Landauer-Büttiker formalism yield a four-conductance state characterized by sizable positive tunnel magnetoresistances (TMR) and tunnel electroresistances (TER). The conductances depend crucially on the details of the electronic structure at the interfaces. In particular, the spin polarization of the tunneling electronic states is affected by the hybridization of orbitals and the associated charge transfer at both interfaces. Digital doping of the PbTiO₃ barrier with Zr impurities at the TiO₂/Co₂ interface removes the excessive metalization of the barrier and significantly enhances the TMR but is not sufficient to switch the TMR\'s sign. Our results indicate that the origin of the TMR inversion might be attributed to the magnetoelectrically active LaSrMnO₃/PbZr_0.2Ti_0.8O₃ interface.