For single longitudinal-mode lasers, the phase and frequency noises are very important parameters for their applications. The passive self-homodyne technique with an unbalanced Michelson interferometer is demonstrated to measure the phase and frequency noise characteristics. The Michelson interferometer for measurements is composed of a 3×3 optical fiber coupler and two Faraday rotator mirrors. The measurement performance is derived and discussed strictly from the transmission matrix of the coupler. The influence to the demodulation resulting from the asymmetry of the 3×3 optical fiber coupler is eliminated through the derived relationship between the differential phase fluctuation and the interferometer fringes. The technique is utilized to measure the phase and frequency noise features of a distributed feedback fiber laser. Based on the measured frequency noise spectrum, the lineshape, linewidth, and phase-error variance related to the laser coherence are able to be calculated and discussed well.