We propose a hybrid spatiotemporal three-dimensional phase unwrapping algorithm for use in digital speckle pattern interferometry (DSPI). The feature of the proposed algorithm is the integration of one-dimensional temporal and two-dimensional spatial phase unwrapping algorithms. By demodulating the phase on a single reference point or multiple reference points using temporal phase unwrapping and on each separated phase map region using spatial phase unwrapping, the DSPI with the spatiotemporal three-dimensional phase unwrapping algorithm can realize the measurement of dynamic absolute displacements and the determination of abrupt phase changes which are usually caused by object discontinuities. We demonstrate that the presented algorithm can overcome the drawbacks of the traditional spatial and temporal phase unwrapping algorithms.