Electrical properties of Josephson junctions Nb/FeSi/Nb with superconductor/ferromagnet (S/F)interfaces are presented. Due to Andreev reflection the nearly exact quadruple enhancement of the tunnel junction differential conductance compared with that of the normal state was achieved. The transparency of the S/F interfaces in our junctions was estimated to be close to unity. This almost ideal value is obtained due to the use of a very smooth amorphous magnetic FeSi alloy for the barrier preparation. The real structure of the Nb/FeSi/Nb tunnel junction is described as a S/F/I/F/S junction. Also Nb/FeSi/Si/Nb Josephson junctions were investigated and the results found on these junctions confirm the effects observed in Nb/FeSi/Nb.