The connection between the columnar growth and evolution of the wavy interface morphology in amorphous and polycrystalline multilayers was investigated by transmission electron microscopy. The material systems of amorphous Si/Ge and polycrystalline Ag/Cu multilayers were chosen as model materials for the investigation. A systematic study of the growth morphology was performed on periodic multilayers as a function of the multilayer period with individual layer thickness up to 50 nm. In comparison with numerous former reports on a wide variety of multilayers, different both in the component elements and preparation methods, the following results proved to be a general property of columnar growth in multilayered thin films. In amorphous and polycrystalline multilayers the diameter of columns (D) depends on the thickness of the thicker layer (H) as D = 3H + 7 nm if the layer thickness does not exceed 16 nm. In both amorphous and polycrystalline multilayers the minima of the wavy interface morphology coincide with the column boundaries, consequently the lateral length of the interface waves depends on H the same way as D. In multilayers where the layer thickness exceeds 16 nm a similar coincidence of column walls and interface minima can be observed in the vicinity of the substrate. However, far from the substrate the evolution of the columnar structure and interface waves can discouple, and the observed layer thickness dependence is preserved only for the interface waves. For the explanation of the observed rule effects of deposition parameters, impurities, grain boundaries in polycrystalline films, and growth instability are discussed.