Heteroepitaxially grown bilayers of ferromagnetic La$_{0.7}$Ca$_{0.3}$MnO$_3$ (LCMO) on top of superconducting YBa$_2$Cu$_3$O$_7$ (YBCO) thin films were investigated by focusing on electric transport properties as well as on magnetism and orbital occupation at the interface. Transport measurements on YBCO single layers and on YBCO/LCMO bilayers, with different YBCO thickness $d_Y$ and constant LCMO thickness $d_L=50$,nm, show a significant reduction of the superconducting transition temperature $T_c$ only for $d_Y<10$,nm,with only a slightly stronger $T_c$ suppression in the bilayers, as compared to the single layers. X-ray magnetic circular dichroism (XMCD) measurements confirm recently published data of an induced magnetic moment on the interfacial Cu by the ferromagnetically ordered Mn ions, with antiparallel alignment between Cu and Mn moments. However, we observe a significantely larger Cu moment than previously reported, indicating stronger coupling between Cu and Mn at the interface. This in turn could result in an interface with lower transparency, and hence smaller spin diffusion length, that would explain our electric transport data, i.e.smaller $T_c$ suppression. Moreover, linear dichroism measurements did not show any evidence for orbital reconstruction at the interface, indicating that a large change in orbital occupancies through hybridization is not necessary to induce a measurable ferromagnetic moment on the Cu atoms.
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