The possibility of dual magnetic and electric tuning of resonance frequencies of the electrodynamic structure consisting of dielectric resonator and the epitaxial film of Yittrium-Iron Garnet (YIG)- lead zirconate titanate (LZT) heterostructure has been shown. The coupled electromagnetic-andspin oscillations of dielectric resonator and epitaxial YIG film were theoretically and experimentally investigated. The experiments revealed the possibility of implementing the electric frequency tuning of coupled oscillations of a composite magnetodielectric resonator. This possibility is determined by induced elastic stresses in the epitaxial YIG film. A theoretical model is proposed for calculating the frequency shift of coupled oscillations caused by the electric field applied to the piezodielectric layer. It is shown that the basic Q-factor of composite resonator and the range of electric frequency tuning of hybrid oscillations increase with the reduction of the magnetic bias field.