We have observed giant magnetoresistance in [Ni80Fe20/Cu/Co/Cu] multilayers with well-defined oscillations in magnitude as a function of the Cu layer thickness both at 300 and 4.2 K. The phase and period are found to be very similar to those previously measured in Co/Cu and, more recently, Ni81Fe19/Cu multilayers. However, the existence of a strong contrast in coercive fields between Ni80Fe20, and Co leads to a significant magnetoresistance for Cu layer thicknesses where coupling is zero or even moderately ferromagnetic. At room temperature, resistance changes as large as 7% are observed within a few tens of oersted of zero field