Epitaxial multiferroic BaTiO3-BiFeO3 composite thin films exhibit a correlation between the magnetoelectric (ME) voltage coefficient αME and the oxygen partial pressure during growth. The ME coefficient αME reaches high values up to 43 V/(cm·Oe) at 300 K and at 0.25 mbar oxygen growth pressure. The temperature dependence of αME of the composite films is opposite that of recently-reported BaTiO3-BiFeO3 superlattices, indicating that strain-mediated ME coupling alone cannot explain its origin. Probably, charge-mediated ME coupling may play a role in the composite films. Furthermore, the chemically-homogeneous composite films show an oxygen vacancy superstructure, which arises from vacancy ordering on the {111} planes of the pseudocubic BaTiO3-type structure. This work contributes to the understanding of magnetoelectric coupling as a complex and sensitive interplay of chemical, structural and geometrical issues of the BaTiO3-BiFeO3 composite system and, thus, paves the way to practical exploitation of magnetoelectric composites.