Using polarized neutron reflectometry (PNR) we have investigated a YBa2Cu3O7(10nm)/La2/3Ca1/3MnO3(9nm)]10 (YBCO/LCMO) superlattice grown by pulsed laser deposition on a La0.3Sr0.7Al0.65Ta0.35O3 (LSAT) substrate. Due to the high structural quality of the superlattice and the substrate, the specular reflectivity signal extends with a high signal-to-background ratio beyond the fourth order superlattice Bragg peak. This allows us to obtain more detailed and reliable information about the magnetic depth profile than in previous PNR studies on similar superlattices that were partially impeded by problems related to the low temperature structural transitions of the SrTiO3 substrates. In agreement with the previous reports, our PNR data reveal a strong magnetic proximity effect showing that the depth profile of the magnetic potential differs significantly from the one of the nuclear potential that is given by the YBCO and LCMO layer thickness. We present fits of the PNR data using different simple block-like models for which either a ferromagnetic moment is induced on the YBCO side of the interfaces or the ferromagnetic order is suppressed on the LCMO side. We show that a good agreement with the PNR data and with the average magnetization as obtained from dc magnetization data can only be obtained with the latter model where a so-called depleted layer with a strongly suppressed ferromagnetic moment develops on the LCMO side of the interfaces. The models with an induced ferromagnetic moment on the YBCO side fail to reproduce the details of the higher order superlattice Bragg peaks and yield a wrong magnitude of the average magnetization. We also show that the PNR data are still consistent with the small, ferromagnetic Cu moment of 0.25muB that was previously identified with x-ray magnetic circular dichroism and x-ray resonant magnetic reflectometry measurements on the same superlattice.