A "membrane-in-the-middle" optomechanical system is demonstrated using a silicon nitride membrane patterned as a subwavelength grating. The grating has a reflectivity of over 99.8%, effectively creating two sub-cavities, with free spectral ranges of 6 GHz, optically coupled via photon tunneling. Measurements of the transmission and reflection spectra show an avoided crossing where the two subcavities simultaneously come into resonance, with a frequency splitting of 54 MHz. Expressions for the lineshapes of the symmetric and antisymmetric modes at the avoided crossing are derived, and the grating reflection, transmission, absorption, and scattering are inferred through comparison with the experimental data.