In this work, spin transport in ferroelectric tunnel junctions with composite barriers and magnetic electrodes is investigated theoretically using spin-dependent screening theory. The shape of the insulator barrier and the electronic structure of the ferromagnetic electrode inevitably affect the spin transport properties. Interestingly, we find that when the Fermi level approaches the bottom of the minority-spin band of the electrode, an approximately ±100% bidirectional spin-filtering effect can be realized due to the included exchange potential with an appropriate electronic band structure of electrodes. Additionally, electrically induced magnetic reconstruction would occur on the electrode surface due to spin-dependent band bending. Our study significantly deepens the current understanding of spin-dependent screening on metal surfaces and at metal/ferroelectric interfaces and provides a feasible method for achieving the interface magnetoelectric effect.