The interplay between antagonistic superconductivity and ferromagnetism has been a interesting playground to explore the interaction between competing ground states. Although this effect in systems of conventional superconductors is better understood, the framework of the proximity effect at complex-oxide-based superconductor/ferromagnet interfaces is not so clear. The main difficulty originates from the lack of experimental tools capable of probing the interfaces directly with high spatial resolution. Here we harness cross-sectional scanning tunnelling microscopy and spectroscopy together with atomic-resolution electron microscopy to understand the buried interfaces between cuprate and manganite layers. The results show that the fundamental length scale of the electronic evolution between YBa2Cu3O(7-δ) (YBCO) and La2/3Ca1/3MnO3 (LCMO) is confined to the subnanometre range. Our findings provide a complete and direct microscopic picture of the electronic transition across the YBCO/LCMO interfaces, which is an important step towards understanding the competition between ferromagnetism and superconductivity in complex-oxide heterostructures.