We study the origin of the magnetoelectric coupling in manganite films on ferroelectric substrates. We find large magnetoelectric coupling in La0.7Ca0.3MnO3/BaTiO3 ultra-thin films in experiments based on the converse magnetoelectric effect. The magnetization changes by around 30-40% upon applying electric fields on the order of 1 kV/cm to the BaTiO3 substrate, corresponding to magnetoelectric coupling constants on the order of α = (2-5) · 10(-7) s/m. Magnetic anisotropy is also affected by the electric field induced strain, resulting in a considerable reduction of coercive fields. We compare the magnetoelectric effect in pre-poled and unpoled BaTiO3 substrates. Polarized neutron reflectometry reveals a two-layer behavior with a depressed magnetic layer of around 30 Å at the interface. Magnetic force microscopy (MFM) shows a granular magnetic structure of the La0.7Ca0.3MnO3. The magnetic granularity of the La0.7Ca0.3MnO3 film and the robust magnetoelastic coupling at the La0.7Ca0.3MnO3/BaTiO3 interface are at the origin of the large magnetoelectric coupling, which is enhanced by phase separation in the manganite.