This paper introduces tunable-contrast fiber-optic polarization interferometer structures arranged in a Michelson configuration. One proposed structure is based on free-space optical alignment and another one is an all-fiber version. Our key idea for achieving the polarization insensitivity during the calibration process is to fix the analyzer at the output port of the polarization interferometer and to vary the incoming polarized optical beam via a fiber-optic polarization controller (FPC). In addition, the polarization rotation and phase retardation controlled by the FPC can be used to determine the loss and phase coefficients of the test sample. Experimental proof of concept for the free-space version indicates a low polarization dependent loss of 0.2 dB. The measured optical loss of 6.38 dB is also determined, limited mainly by the fiber connectors, reflection loss, and the fixed 45° analyzer. In addition, tunability of the fringe contrast is obtained by varying the incoming polarized optical beam.