The current-perpendicular-to-plane (CPP) magnetoconductoance of a sample sandwiched by two ideal non-magnetic leads is described at an ab initio level. The so-called 'active' part of the system is a trilayer consisting of two magnetic slabs of finite thickness separated by a non-magnetic spacer. We use a transmission matrix formulation of the conductance based on surface Green functions as formulated by means of tight-binding linear muffin-tin orbital method. An equivalent and computationally more efficient formulation of the problem based on reflection matrices is also presented. The formalism is extended to the case of lateral supercells with random arrangements of atoms which in turn allows to deal with ballistic and diffusive trnsport on equal footing. Applications refer to fcc-based Co/Cu/Co(001) trilayers.