We report the ferroelectric, ferromagnetic, and magnetoelectric ͑ME͒ properties of self-assembled epitaxial BiFeO 3 -CoFe 2 O 4 ͑BFO-CFO͒ nanostructure composite thin films deposited on ͑001͒, ͑110͒, and ͑111͒ SrTiO 3 ͑STO͒ single crystal substrates. These various properties are shown to depend on orientation. The maximum values of the relative dielectric constant, saturation polarization, longitudinal piezoelectric coefficient, saturation magnetization, and ME coefficient at room temperature were 143, 86 m / cm 2 , 50 pm/V, 400 emu/cc, and 20 mV/ cm Oe, respectively.