Interferometers are essential elements in classical and quantum optical systems. The strictly required stability when extracting the phase of photons is vulnerable to polarization variation and phase shift induced by environment disturbance. Here, we implement polarization-insensitive interferometers by combining silica planar light-wave circuit chips and Faraday rotator mirrors. Two asymmetric interferometers with temperature controllers are connected in series to evaluate the single-photon interference. Average interference visibility over 12 h is above 99%, and the variations are less than 0.5%, even with active random polarization disturbance. The experiment results verify that the hybrid chip is available for high-demand applications like quantum key distribution and entanglement measurement.