Metallic multilayers with giant magnetoresistance (GMR) effect is all active research field. GMR is governed by several physical parameters. In this paper, one of the most important parameters, surface and interface roughness is investigated. The Co/Cu multilayers on Si(111) and Si(100) with a Cr buffer layer were grown by electron beam evaporation in one run. Auger depth profiling, grazing incidence X-ray reflectivity and Atomic Force Microscopy clearly demonstrate the structural difference in the two Co/Cu multilayer samples. The multilayers on Si(111) have smoother surface and interfaces, while the multilayers on Si(100) have rougher surface and interfaces, which originates from the different surface roughness of the Si(111) and Si(100) substrates, 0.36 and 0.68 nm respectively. The surface evolution of the multilayers during deposition is also discussed.