Recent magnetic measurements at La0.67Ca0.33MnO3/YBa2Cu3O7 interfaces led to conflicting interpretations: a magnetic "dead" layer on the LCMO side or antiparallel Cu and Mn magnetic moments. Here we report results of first-principles density-functional calculations of position-dependent magnetic couplings between interlayer and intralayer Mn atoms. The couplings in the first few layers near the interface are found to be weak ferromagnetic or even antiferromagnetic. The results suggest that a "dead" magnetic layer 2-3 atoms thick is present, as needed to account for the observations.