We demonstrate experimentally, for the first time, the feasibility of passively enhancing fluorescence and Raman signals from diffusely scattering media in a conventional backscattering collection geometry. The method employs transmission of the collimated excitation laser beam through a "unidirectional" dielectric mirror placed directly in front of the sample. This permits laser light that escapes from the sample surface to be reflected back into the sample where it can be more usefully employed in generating Raman and fluorescence signals. This leads to improved Raman signal, higher signal-to-noise ratio, and shorter acquisition times. Feasibility studies performed on standard pharmaceutical tablets and on sheets of Teflon, using a single enhancing element, demonstrate signal enhancement factors of 6 (fluorescence) and 3 (Raman). Potential applications of this simple device include improving quality control of pharmaceutical products, disease diagnosis of biological tissue, forensics, and security screening.