We propose a novel concept for creating high-g cavities in photonic crystal slabs (PCS). These cavities are formed by depositing a polymer layer on top of a photonic crystal membrane fabricated in a high index semiconductor slab. We show that such multilayer structures exhibit a mode-gap and can yield high-Q microcavities with quality factors of Q-106. This allows the cavity to be created by polymer processing, following the much more demanding semiconductor processing that is used to generate a uniform PCS. Depending on the polymer used, these structures can be additionally tuned using photosensitivity or the electro-optic effect.