Ferrimagnetic CoFe2O4 nanopillars embedded in a ferroelectric BaTiO3 matrix are an example for a two-phase magnetoelectrically coupled system. They operate at room temperature and are free of any resource-critical rare-earth element, which makes them interesting for potential applications. Prior studies succeeded in showing strain-mediated coupling between the two subsystems. In particular, the electric properties can be tuned by magnetic fields and the magnetic properties by electric fields. Here we take the analysis of the coupling to a new level utilizing soft X-ray absorption spectroscopy and its associated linear dichroism. We demonstrate that an in-plane magnetic field breaks the tetragonal symmetry of the (1,3)-type CoFe2O4/BaTiO3 structures and discuss it in terms of off-diagonal magnetostrictive-piezoelectric coupling. This coupling creates staggered in-plane components of the electric polarization, which are stable even at magnetic remanence due to hysteretic behaviour of structural changes in the BaTiO3 matrix. The competing mechanisms of clamping and relaxation effects are discussed in detail.