We study theoretically the coupled multiferroic dynamics of a finite one-dimensional ferroelectric/ferromagnet chain driven by harmonic magnetic and electric fields as a function of the chain length. We consider the case of a linear magnetoelectric coupling that results from the spin-polarized screening charge at the interface. We performed Monte-Carlo simulations and calculations based on the coupled Landau-Lifshitz-Gilbert and Landau-Khalatnikov equations showing that the net magnetization and the total polarization of thin heterostructures, i.e. with up to ten ferroelectric and ferromagnetic sites counted from the interface, can be completely reversed by external electric and magnetic fields, respectively. However, for larger systems merely a limited magnetoelectrical control is achievable.