Interferometric phase restoration is a crucial step in retrieving large-scale geophysical parameters from Synthetic Aperture Radar (SAR) images. Existing noise impacts the accuracy of parameter retrieval as a result of decorrelation effects. Most state-of-the-art filtering methods belong to the group of nonlocal filters. In this paper, we propose a novel convolutional sparse coding method in complex domain with the prior knowledge of coherence integrated into the optimization model, which is termed as CoComCSC. CoComCSC is not only capable of reducing noise in regions with continuous phase changes, but also of preserving the phase details prominently. The experiments results on simulated and real data demonstrate the effectiveness of CoComCSC by comparing with other state-of-the-art methods. Moreover, the obtained Digital Elevation Model (DEM) product by CoComCSC from RADARSAT-2 data indicates its superior filtering performance over regions with heterogeneous land-covers, which shows its great potential for generating high-resolution DEM products.