Room-temperature magnetoelectric (ME) coupling is developed in artificial multilayers and nanocomposites composed of magnetostrictive and electrostrictive materials. While the coupling mechanisms and strengths in multilayers are widely studied, they are largely unexplored in vertically aligned nanocomposites (VANs), even though theory has predicted that VANs exhibit much larger ME coupling coefficients than multilayer structures. Here, strong transverse and longitudinal ME coupling in epitaxial BaTiO3:CoFe2O4 VANs measured by both optical second harmonic generation and piezoresponse force microscopy under magnetic fields is reported. Phase field simulations have shown that the ME coupling strength strongly depends on the vertical interfacial area which is ultimately controlled by pillar size. The ME coupling in VANs is determined by the competition between the vertical interface coupling effect and the bulk volume conservation effect. The revealed mechanisms shed light on the physical insights of vertical interface coupling in VANs in general, which can be applied to a variety of nanocomposites with different functionalities beyond the studied ME coupling effect.