An instrument for noncontact measurement of differential vibrations is developed, based on the self-mixing interferometer. As no reference arm is available in the self-mixing configuration, the differential mode is obtained by electronic subtraction of signals from two (nominally equal) vibrometer channels, taking advantage that channels are servo stabilized and thus insensitive to speckle and other sources of amplitude fluctuation. We show that electronic subtraction is nearly as effective as field superposition. Common-mode suppression is 25-30 dB, the dynamic range (amplitude) is in excess of 100 microm, and the minimum measurable (differential) amplitude is 20 nm on a B = 10 kHz bandwidth. The instrument has been used to measure vibrations of two metal samples kept in contact, revealing the hysteresis cycle in the microslip and gross-slip regimes, which are of interest in the study of friction induced vibration damping of gas turbine blades for aircraft applications.