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The current-perpendicular-to-plane (CPP) magnetoconductance of a trilayer consisting of a spacer sandwiched between two ideal leads is described on anab initio level. We employ the transmission matrix formulation of the conductance within the framework of the spin-polarized surface Green function technique as formulated in terms of the tight-binding linear muffin-tin orbital method. The formalism is extended to the case of lateral supercells in each layer with random arrangements of atoms which allows to treat both the ballistic and diffusive transports on equal footing. The application is made to fcc-based Co/Cu/Co(001) trilayers.