Multiferroics are singular materials that can display simultaneously electric and magnetic orders. Some of them can be ferroelectric and ferromagnetic and, for example, provide the unique opportunity of encoding information independently in electric polarization and magnetization to obtain four different logic states. However, schemes allowing a simple electrical readout of these different states have not been demonstrated so far. In this article, we show that this can be achieved if a multiferroic material is used as the tunnel barrier in a magnetic tunnel junction. We demonstrate that thin films of ferromagnetic-ferroelectric La0.1Bi0.9MnO3 (LBMO) retain both ferroic properties down to a thickness of only 2 nm. We have used such films as spin-filtering tunnel barriers the magnetization and electric polarization of which can be switched independently. In that case, the tunnel current across the structure is controlled by both the magnetic and ferroelectric configuration of the barrier, which gives rise to four distinct resistance states. This can be explained by the combination of spin filtering by the ferromagnetic LBMO barrier and the partial charge screening of electrical charges at the barrier/electrode interfaces due to ferroelectricity. We anticipate our results to be a starting point for more studies on the interplay between ferroelectricity and spin-dependent tunneling, and for the use of nanometric multiferroic elements in prototype devices. On a wider perspective, they may open the way towards novel reconfigurable logic spintronics architectures and to electrically controlled readout in quantum computing schemes using the spin-filter effect.