  Cavity-optomechanics enables photon-phonon interaction and correlations by
harnessing the radiation-pressure force. Here, we realize a
``cavity-in-a-membrane'' optomechanical architecture which allows detection of
the motion of lithographically-defined, ultrathin membranes via an integrated
optical cavity. Using a dissipative filtering method, we are able to eliminate
the probe light in situ and observe photon-phonon correlations associated with
the low-frequency membrane mechanical mode. The developed method is generally
applicable for study of low-frequency light scattering processes where
conventional frequency-selective filtering is unfeasible.
