Phase unwrapping (PU) is among the most critical tasks in synthetic aperture radar (SAR) interferometry (InSAR). Due to the presence of noise, the interferogram usually presents phase inconsistencies, also called residues, which imply a nonunivocal solution. This work investigates the PU problem from a semantic segmentation perspective by exploiting convolutional neural network (CNN) models. In particular, by exploiting a popular deep-learning architecture, we introduce the interferometric coherence as an input feature and analyze the performance increase against classical methods. For the network training, we generate a variegated data set by introducing a controlled number of phase residues, and considering both synthetic and real InSAR data. Eventually, we compare the proposed method to state-of-the-art algorithms on synthetic and real InSAR data taken from the TanDEM-X mission, obtaining encouraging results.