$\mathrm{YBa_2Cu_3O_7/La_{2/3}Ca_{1/3}MnO_3}$ superconducting/ferromagnetic (SC/FM) multilayers have been studied by neutron reflectometry. Evidence for a characteristic difference between the structural and magnetic depth profiles is obtained from the occurrence of a structurally forbidden Bragg peak in the FM state. The comparison with simulated reflectivity curves allows us to identify two possible magnetization profiles: a sizable magnetic moment within the SC layer antiparallel to the one in the FM layer (inverse proximity effect), or a ``dead'' region in the FM layer with zero net magnetic moment. The former scenario is supported by an anomalous SC-induced enhancement of the off-specular reflection, which testifies to a strong mutual interaction of SC and FM order parameters. Comment: 4 pages, 2 figures, submitted to PRL