We report the direct imaging of the magnetic response of a 4.8 nm La_0,9Ba_0.1MnO₃ film to the voltage applied across a 5 nm BaTiO₃ film in a BaTiO₃/La_0,9Ba_0.1MnO₃ multiferroic heterostructure using x-ray photoemission electron microscopy (XPEEM). Specifically, we have written square ferroelectric domains on the BaTiO₃ layer with an atomic force microscope in contact mode and imaged the corresponding magnetic contrast through the x-ray circular dichroic effect at the Mn L-edge with high spatial lateral resolution using XPEEM. We find a sudden decrease in the magnetic contrast for positive writing voltages above +6 V associated with the switching of the ferroelectric polarization of the BaTiO₃, consistent with the presence of a magnetoelectric effect through changes in the hole carrier density at the BaTiO₃/La_0,9Ba_0.1MnO₃ interface. Temperature-dependent measurements show a decrease in the Curie temperature and magnetic moment in the areas where a positive voltage above +6 V was applied, corresponding to the hole depletion state and suggesting the onset of a spincanted state of bulk La_0,9Ba_0.1MnO₃. Our results are the first direct imaging of magnetoelectric coupling in such multiferroic heterostructure.