The interaction between superconductivity and magnetism in spatially confined heterostructures of thin film multilayers is investigated in the ferromagnetic manganite La2/3Ca1/3MnO3 (LCMO) and the high-temperature superconductor YBa2Cu3O7-δ (YBCO) mediated by an intermediate insulating SrTiO3 (STO) layer. The STO layer is used to mediate and tune the range of interactions between the ferromagnet and superconductor. A magnetically depleted layer with zero-magnetisation within the LCMO layer is shown by polarised neutron reflectometry measurements. This zero-magnetisation layer is caused by the onset of superconductivity in YBCO despite being separated by an insulating layer with a thickness much larger than the superconducting coherence length. The magnetic field dependence of this interaction is also explored. We show that the magnetism of the depleted layer can be restored by applying a magnetic field that partially destroys the superconductivity in YBCO, restricting the electronic interaction between the materials.