We have studied the dependence of impurity vs. band effects in the appearance of inverse giant magnetoresistance (IGMR) in Cu/Fe superlattices with Cr. Current in plane (CIP) and current perpendicular to the plane (CPP) geometies are considered. For the calculation of the conductivities we have used the linearized Boltzmann equation in the relaxation times and the band effects through the semiclassical velocities obtained from the LDA calculated electronic structure. The larger the Cr/Fe hybridization strength, the bigger is the tendency towards IGMR. In particular, in CIP geometry roughness at these interfaces increases the IGMR range. The calculated GMR ratios have been compared with the experimental results. From this comparison we conclude that the experimental data can only be explained by taking into account Cr bands.