Magnetoresistance curves have been measured for 80 Å Ni 80Fe20/tCu Cu/60 Å Ni80Fe 20/80 Å Fe50Mn50 layered systems (t Cu=9-93 Å). 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 tCu. The interplay of this coupling with the exchange biasing effect results in a critical interlayer thickness, t critCu=15 Å, 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 tcrit Cu. Indeed, such a maximum was found (with ΔR/R=4.3%) at t Cu=22 Å, a value well above tcritCu. This is attributed to the occurence of inhomogeneities in the interlayer exchange coupling.