Room temperature deposition of single and multiple layers of silicon and molybdenum has been explored in vacuo by scanning tunneling microscopy at growth conditions used for typical Mo/Si multilayer optics, enabling the study of the topography down to the nanometer scale. Periodic Mo/Si multilayer films with a molybdenum layer thickness of 2.5 nm and a silicon layer thickness of 5 nm show an evolution of the surface roughness that is similar to polycrystalline film self-affine growth. By applying an ion beam treatment of the silicon layers this increase of the roughness with layer thickness is completely mitigated, yielding a final roughness of the entire stack similar to that of the first ion treated silicon layer. The ion treatment step used here is most efficient in reducing surface roughness at lateral length scales between 5-10 nm. Polycrystalline growth of molybdenum on this ion treated silicon layer is observed only when the layer exceeds 3 nm thickness, while smaller amounts of molybdenum do not significantly increase the surface roughness. The almost identical values for the roughness of ion treated silicon and the 2.5 to 3 nm molybdenum grown on top of ion treated silicon show that the roughness of Si-on-Mo and Mo-on-Si interfaces have a similar contribution to the optical performance of Mo/Si multilayer films. Interface roughness accounts for approximately 40% of the multilayer reflectance loss when compared to reflectance calculations of perfectly structured multilayers.