Boosting nonlinear frequency-conversion efficiencies in hybrid metal-dielectric nanostructures generally requires the enhancement of optical fields that interact constructively with nonlinear dielectrics. Inevitably for localized surface plasmons, spectra subject to this enhancement tend to span narrowly. As a result, because of the spectral mismatch of resonant modes at frequencies participating in nonlinear optical processes, strong nonlinear signal generations endure the disadvantage of rapid degradations. Here, we experimentally design a multiband enhanced second-harmonic generation platform of three-dimensional metal-dielectric-metal nanocavities that consist of thin ZnO films integrated with silver mushroom arrays. Varying geometric parameters, we demonstrate that the introduction of ZnO materials in intracavity regions enables us to modulate fundamental-frequency-related resonant modes, resulting in strong coupling induced plasmon hybridization between localized and propagating surface plasmons. Meanwhile, ZnO materials can also serve as an efficient nonlinear dielectric, which provides a potential to obtain a well-defined coherent interplay between hybridized resonant modes and nonlinear susceptibilities of dielectric materials at multi-frequency. Finally, not only is the conversion efficiency of ZnO materials increased by almost two orders of magnitude with respect to hybrid un-pattered systems at several wavelengths over a 100-nm spectral range but also a hybrid plasmon-light coupling scheme in three-dimensional nanostructures can be developed.