We propose a demodulation technique for a multiplexed fiber Fizeau interferometer (FFI) and fiber Bragg grating (FBG) sensor system using the discrete wavelet transform with signal processing enhancements. This simple and flexible demodulation technique determines the cavity length of FFI and the Bragg wavelength of FBG simultaneously and is especially suited for quasi-static measurements. We demonstrate this demodulation technique by performing some strain measurements, and a strain resolution of 1.0 microepsilon and an accuracy of 2.6 microepsilon are obtained. The maximum cross-talk of the sensor system is 6% of the applied strains.