Coupling between superconducting and ferromagnetic states in hybrid oxide heterostructures is presently a topic of intense research. Such a coupling is due to the leakage of the Cooper pairs into the ferromagnet. However, tunneling of the Cooper pairs though an insulator was never considered plausible. Using depth sensitive polarized neutron reflectivity we demonstrate the coupling between superconductor and magnetic layers in epitaxial La2/3Ca1/3MnO3 (LCMO)/SrTiO3/YBa2Cu3O7-δ (YBCO) hybrid heterostructures, with SrTiO3 as an intervening oxide insulator layer between the ferromagnet and the superconductor. Measurements above and below the superconducting transition temperature (TSC) of YBCO demonstrate a large modulation of magnetization in the ferromagnetic layer below the TSC of YBCO in these heterostructures. This work highlights a unique tunneling phenomenon between the epitaxial layers of an oxide superconductor (YBCO) and a magnetic layer (LCMO) through an insulating layer. Our work would inspire further investigations on the fundamental aspect of a long range order of the triplet spin-pairing in hybrid structures.