Multiferroic heterostructures comprising ferroelectric and ferro(ferri)magnetic constituents have recently attracted considerable interest due to the strong coupling between magnetic and electric properties which may have interesting applications. Here we investigate the magnetoelectric coupling at the ferrimagnetic/ferroelectric Fe3 O4 / BaTiO3 (001) interfaces within the framework of density-functional theory. The coupling in this system originates from the interface bonding sensitive to atomic displacements at the interface and leads to the change in the interface magnetization when the polarization of the ferroelectric layer reverses. We consider two types of interface terminations of Fe3 O4 which have different iron cation valence and oxygen atom environment. We find that the magnitude of the magnetoelectric coupling is stronger for the oxygen-deficient Fe3 O4 / BaTiO3 (001) interface. The sensitivity to the interface oxygen content suggests that oxidation or oxygen vacancies at the interface may play an important role in determining the strength of the interface magnetoelectric coupling. © 2008 The American Physical Society.