Transmission electron microscopy images and hard x-ray reflectivity curves are used to obtain information on the growth characteristics of x-ray multilayer mirrors. A multi-resolution approach based on wavelet analysis is used to decompose the interface profiles obtained from transmission electron microscopy images into a number of different spatial frequency ranges. The replication factor (vertical) and the characteristic length (lateral) of the interfacial roughness are determined in these spatial frequency ranges. By changing the upper or lower limits of the wavelet transform of the x-ray reflectivity curves, the structure uniformity (lateral) and evolution of the surface damage (vertical) are determined. These results are significant for the study of the growth characteristics of ultrathin x-ray multilayer mirrors and enable more effective methods to determine their imperfections.