Laser interferometry is the technique of choice for studying the smallest displacements of the hearing organ. For low intensity sound stimulation, these displacements may be below 1 nm. This cannot be reliably measured with other presently available techniques in an intact organ of Corti. In a heterodyne interferometer, light is projected against an object of study and motion of the target along the optical axis causes phase and frequency modulations of the back-reflected light. To recover object motion, the reflected light is made to interfere with a reference beam of artificially altered frequency, producing a beating signal. In conventional interferometers, this carrier signal is demodulated with analog electronics. In this paper, we describe a digital implementation of the technique, using direct carrier sampling. In order to obtain the necessary reference signal for demodulation we introduce an additional third light path. Together, this results in lower noise and reduces the cost of the system. Within the hearing organ, different structures may move in different directions. It is therefore necessary to precisely measure the angle of incidence of the laser light, and to precisely localize the anatomical structure where the measurement is performed. Therefore, the interferometer is integrated with a laser scanning confocal microscope that permits us to map crucial morphometric parameters in each experiment. We provide key construction parameters and a detailed performance characterization. We also show that the system accurately measures the diminutive vibrations present in the apical turn of the cochlea during low-level sound stimulation.