The schematic and results of studying an interferometer for a wavelength of 8 mm with homodyne frequency conversion for measuring the electron density of a steady-state plasma are described. The design of its waveguide system allows the drift of the indicated initial phase to be reduced to a level of +/- 0.1 degrees/h. The maximum phase shift measured is 360 degrees, the tolerable signal-power decay in plasma is 16 dB, and the maximum phase measurement error is similar to 5%.