Thin-film oxide heterostructures show great potential for use in spintronic memories, where electronic charge and spin are coupled to transport information. Here we use a La_0.7Sr_0.3MnO₃ (LSMO)/PbZr_0.2Ti_0.8O₃ (PZT) model system to explore how local variations in electronic and magnetic phases mediate this coupling. We present direct, local measurements of valence, ferroelectric polarization and magnetization, from which we map the phases at the LSMO/PZT interface. We combine these experimental results with electronic structure calculations to elucidate the microscopic interactions governing the interfacial response of this system. We observe a magnetic asymmetry at the LSMO/PZT interface that depends on the local PZT polarization and gives rise to gradients in local magnetic moments; this is associated with a metal–insulator transition at the interface, which results in significantly different charge-transfer screening lengths. This study establishes a framework to understand the fundamental asymmetries of magnetoelectric coupling in oxide heterostructures.