A multiferroic heterostructure is constructed by growing an epitaxial piezoelectric $\mathrm{Pb}({\mathrm{Zr}}_{0.3},{\mathrm{Ti}}_{0.7}){\mathrm{O}}_{3}$ film on a magnetostrictive layered manganite single crystal of composition ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$. The efficient mechanical coupling at the interface results in a remarkable magnetoelectric (ME) effect. The ME voltage is $\ensuremath{\sim}87%$ of the theoretical value predicted by a phenomenological thermodynamic model. The ME effect peaks at the ferromagnetic transition temperature of the manganite, a consequence of its magnetostrictive characteristics.