The spin-polarized electron conductance perpendicular to layers of a random magnetic multilayer is evaluated from first principles. We employ the Landauer formulation in the framework of the tight-binding linear muffin-tin orbital approach and the surface Green-function technique. The disorder in the bulk and at interfaces is included in terms of lateral supercells confined to individual atomic layers. The application is made to interleave and separate multilayers with a different order of magnetic and non-magnetic layers with generally non-collinear alignments of layer magnetizations.