The magnetoresistance (MR) of magnetic multilayers formed by electrodeposition of Co and Cu in the parallel pores of nanoporous polycarbonate membranes was measured in the current-perpendicular-to-plane (CPP-MR) geometry, with Co acid Cu thicknesses in the range 2-50 nm. Ratios reaching 20% at ambient temperature and 30% at 20 K were obtained. A systematic study of the magnetoresistance as a function of the Co and Cu thicknesses was interpreted in terms of a two-current model. The volume and interface resistance asymmetry parameters could be deduced and the ability to determine the spin diffusion length by this method was discussed. An estimate of the Cu spin flip length has been found. Comparison of the data at 20 and 300 K showed that the product of the resistance change and the maximum resistance is temperature invariant.