This paper presents results showing that the design of substrates used for surface-enhanced Raman spectroscopy (SERS) can impact the apparent enhancement factors (EFs) obtained due to optical interference effects that are distinct from SERS, providing additional enhancement of the Raman intensity. Thus, a combination of SERS and a substrate designed to maximize interference-based enhancement is demonstrated to give additional Raman intensity above that observed for SERS alone. The system explored is 4-nitroazobenzene (NAB) and biphenyl (BP) chemisorbed on a nanostructured silver film obtained by vacuum deposition of Ag on thermally oxidized silicon wafers. The enhancing silver layer is partially transparent, enabling a standing wave to form as a result of the combination of the incident light and light reflected from the underlying Si substrate (i.e., light that passes through the Ag and the intervening dielectric layer of SiOx). The Raman intensity is measured as a function of the thickness of the thermal oxide layer in the range from ∼150 to ∼400 nm, and despite a lack of morphological variation in the silver films, there is a strong dependence of the Raman intensity on the oxide thickness. The Raman signal for the optimal SiO_x interlayer thickness is 38 times higher than the intensity obtained when the Ag particles are deposited directly onto Si (with native oxide). To account for the trends observed in the Raman intensity versus thickness data, calculations of the relative mean square electric field (MSEF) at the surface of the SiO_x are carried out. These calculations are also used to further optimize the experimental setup.