We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-one-dimensional lattice and to attractive interactions from fermionic atoms that are localized in various configurations inside the lattice wells. The system is treated within a Bose-Hubbard tight binding model by an out-of-equilibrium Green function approach. A new band gap opens up when the lattice period is doubled by locating the fermions in alternate wells and yields an interference pattern in the transmittivity on varying the intensity of the driving force. The positions of the transmittivity minima are determined by matching the period of Bloch oscillations and the time for tunnelling across the band gap. Massive disorder in the distribution of the fermions will wash out the interference pattern. We report illustrative numerical results for a mixture of Rb-87 and K-40 atoms in an optical lattice created by laser beams with a wavelength of 763 nm. The period doubling of the lattice can also be experimentally realized in a four-beam set-up.