Mo/Si multilayer mirrors with nanoscale bilayer thicknesses have been deposited on stepped substrate topographies, using various deposition angles. The multilayer morphology at the stepedge region was studied by cross section transmission electron microscopy. A transition from a continuous-to columnar layer morphology is observed near the step-edge, as a function of the local angle of incidence of the deposition flux. Taking into account the corresponding kinetics and anisotropy in layer growth, a continuum model has been developed to give a detailed description of the height profiles of the individual continuous layers. Complementary optical characterization of the multilayer system using a microscope operating in the extreme ultraviolet wavelength range, revealed that the influence of the step-edge on the planar multilayer structure is restricted to a region within 300 nm from the step-edge.