We have demonstrated extraordinary light transmission effect through Fabry-Peacuterot cavities in multilayered plasmonic crystals formed by coupling two physically separated metallic nanohole and nanodisk array layers. Superior field-medium overlap is observed with Fabry-Peacuterot resonances as a result of stronger electromagnetic field confinement in the dielectric region far from the metallic surfaces. We show that these cavity resonances are highly sensitive to refractive index changes. The large field-material overlap combined with simple fabrication scheme used here makes these structures an ideal candidate for biosensing applications.