Soft x-ray standing waves produced by a multilayer interference substrate add depth-sensitivity to magnetic circular dichroism to resolve changes in Co magnetism across a 10${AA}$ distance from the Co center to the Co-Pd interface of a Pd/Co/Pd trilayer having in-plane magnetization. Large enhancements of in-plane orbital and spin magnetic moments, as well as the number of d holes, are strongly localized in a thin interface layer. These results provide new insight into the phenomenon of magnetic anisotropy at buried interfaces, and suggest a broad applicability of such standing wave measurements to interface magnetism studies.