Magnetoresistance curves have been measured for 80 angstrom Ni80Fe20/t(Cu) Cu/60 angstrom Ni80Fe20/80 angstrom Fe50Mn50 layered systems (t(Cu) = 9-93 angstrom). After separating the contributions from anisotropic magnetoresistance and spin valve or ''giant'' magnetoresistance (GMR), the GMR curves were interpreted in terms of a minimum-energy model for the magnetization orientation of the Ni80Fe20 layers. The interlayer exchange coupling was found to be purely ferromagnetic, and monotonically decreasing with increasing t(Cu). The interplay of this coupling with the exchange biasing effect results in a critical interlayer thickness, t(Cu)crit = 15 angstrom, below which no perfect antiparallel alignment of the Ni80Fe20 magnetizations can be realized. The GMR, which would otherwise increase with decreasing Cu layer thickness, is therefore expected to reach a maximum at or slightly below t(Cu)crit. Indeed, such a maximum was found (with DELTAR/R = 4.3 %) at t(Cu) = 22 angstrom, a value well above t(Cu)crit. This is attributed to the occurence of inhomogeneities in the interlayer exchange coupling.