We apply the frequency-domain interferometry technique in the extreme-ultraviolet (XUV) range using high-order harmonics. The technique is first used to study the influence of ionization of the generating gas on the harmonic emission. We report a thorough study of the fringe contrast as a function of the generating parameters: gas pressure, laser intensity and focus position, harmonic order, delay, and relative intensity of the two laser pulses. We show that two phase-locked time-delayed harmonic pulses can be produced under optimal conditions. However, a strong distortion of the fringe pattern (low contrast and large asymmetry) can be induced by the deleterious effects of the medium ionization, i.e., depletion of the emitters, laser defocusing, and loss of mutual coherence that is due to free-electron dispersion. XUV frequency-domain interferometry is then applied to the measurement of the electron density of a plasma created by optical field-induced ionization of a high-pressure helium jet by use of an intense short-pulse laser. The measured temporal evolution of the electron density shows that the resolution of our experimental setup was of the order of 200 fs, which, to our knowledge, provides the first XUV interferometry measurement on a femtosecond time scale.