This paper describes the design and performance of a phase demodulation scheme based on software-defined radio (SDR), applied in heterodyne interferometry. The phase retrieval is performed in real time by means of a low-cost SDR with a wideband optoelectronic front-end. Compared to other demodulation schemes, the system is quite simpler, versatile, and of lower cost. The performance of the demodulator is demonstrated by measuring the displacement per volt of a thin-film polymeric piezoelectric transducer based on polyvinylidene fluoride for ultrasonic applications. We measured displacements between 3.5 pm and 122 pm with 7% relative uncertainty, in the frequency range from 20 kHz to 1 MHz.