In this paper, we propose and demonstrate a novel interferometer and signal process to retrieve two-dimensional signals with multilevel phases. The interferometer is based on a shearing interferometry with double-frequency grating, and phase-shifting interferometry is derived as a built-in function of the lateral displacement of the grating. The interferometer not only retrieves the multilevel phase signals but also eliminates slow-varying phase errors wherever they occur. Owing to the common path algorithm, the new interferometer is more robust in dynamic circumstances for optical testing and data processing. We propose a pre-integral signal process for two-dimensional (2D) data processing to prevent post-phase-integral due to shearing interferometry. The simulation and experiment showed that the proposed interferometer with a pre-integral process has various advantages in signal processing for multilevel phase retrieval, and will be useful for higher data rates in optical data storage and free-space communication.