A real-space Green-function technique, in which the scattering is trea
ted exactly, is used in a single-band tight-binding model to evaluate
the Ohmic resistivities and the giant magnetoresistance in trilayer sy
stems. The model includes (i) spin dependence of the density of states
and Fermi velocity in the magnetic material, giving a qualitative rep
resentation of Co/Cu and Fe/Cr systems; (ii) spin-independent bulk dis
order, representing intrinsic defects in real systems; (iii) chemicall
y sharp interfacial roughness. It is found that for parameters that pr
oduce realistic total resistivities, the spin-polarized band structure
in conjunction with the spin-independent bulk disorder gives the main
contribution to the giant magnetoresistance. The chemically sharp int
erfacial roughness enhances the effect. Its contribution becomes signi
ficant in the limit of sufficiently dense roughness steps, sufficientl
y weak bulk disorder, and sufficiently thin magnetic layers.