Sub-wavelength high contrast gratings offer the exciting possibility of “membrane-in-the-middle” optomechanics with a low-mass, highly reflective membrane. Theoretical treatments of this system have, to date, employed the model of a zero-thickness polarizable slab. The validity of this model is, however, limited, since in general highly reflective subwavelength gratings do not have an optical thickness that is much smaller than the wavelength of the light employed. In this work, we show that this model in fact makes incorrect predictions concerning the field modes in an optical cavity with a subwavelength grating at the exact center. It predicts that the modes can be classified in doublets, one member of which has an antisymmetric spatial profile and no absorption, the other of which has a symmetric spatial profile and absorptive losses. The situation for a subwavelength grating, however, is quite different: Both modes have absorptive loss, but the mode with the antisymmetric spatial profile has greater loss. In addition, the frequencies of the modes are interchanged: In the case of the zero-thickness slab, the antisymmetric mode has the lower frequency, while in the case of the subwavelength grating, it is the symmetric mode that is the low-frequency member of the doublet. These considerations will be important for a correct interpretation of experimental data as the performance of such sytems continues to improve.