A stable phase demodulation system for diaphragm-based acoustic sensors is reported. The system is based on a modified fiber-optic Sagnac interferometer with a stable quadrature phase bias, which is independent of the parameters of the sensor head. The phase bias is achieved passively by introducing a nonreciprocal frequency shift between the counter-propagating waves, avoiding the use of complicated active servo-control. A 100 nm-thick graphite diaphragm-based acoustic sensor interrogated by the proposed demodulation system demonstrated a minimum detectable pressure level of ~450 µPa/Hz(1/2) and an output signal stability of less than 0.35 dB over an 8-hour period. The system may be useful as a universal phase demodulation unit for diaphragm-based acoustic sensors as well as other sensors operating in a reflection mode.