Heterostructures with competing magnetic interactions are often exploited for their tailored new functionalities. Exchange bias is one such outcome of interfacial coupling across ferromagnetic–antiferromagnetic, multiferroic–ferromagnetic, two antiferromagnetic, or antiferromagnetic and paramagnetic interfaces. Apart from the usual horizontal shift of the hysteresis loop (exchange bias shift), a small `vertical shift' of the hysteresis loops along the magnetization axis has also been seen, but it was always relatively small. Recently, an unusually large `vertical shift' in epitaxial bilayer heterostructures comprising ferromagnetic La0.7Sr0.3MnO3 and multiferroic orthorhombic YMnO3 layers was reported. Here, using polarized neutron reflectometry, the magnetic proximity effect in such bilayers has been investigated. A detailed magnetic depth profile at the interface, elucidating the intrinsic nature of the vertical shift in such heterostructures, is reported. Further corroboration of this observation has been made by means of first‐principles calculations, and the structural and electronic properties of YMnO3/La0.7Sr0.3MnO3 heterostructures are studied. Although in the bulk, the ground state of YMnO3 is an E‐type antiferromagnet, the YMnO3/La0.7Sr0.3MnO3 heterostructure stabilizes the ferromagnetic phase in YMnO3 in the interface region. It is found that, in the hypothetical ferromagnetic phase of bulk YMnO3, the polarization is suppressed, and owing to a large difference between the lattice constants in the ab plane a strong magnetocrystalline anisotropy is present. This anisotropy produces a high coercivity of the unusual ferromagnetic YMnO3 phase at the interface, which is responsible for the large vertical shift observed in experiment.