Phase filtering and pixel quality (coherence) estimation is critical in producing Digital Elevation Models (DEMs) from Interferometric Synthetic Aperture Radar (InSAR) images, as it removes spatial inconsistencies (residues) and immensely improves the subsequent unwrapping. Large amount of InSAR data facilitates Wide Area Monitoring (WAM) over geographical regions. Advances in parallel computing have accelerated Convolutional Neural Networks (CNNs), giving them advantages over human performance on visual pattern recognition, which makes CNNs a good choice for WAM. Nevertheless, this research is largely unexplored. We thus propose "GenInSAR", a CNN-based generative model for joint phase filtering and coherence estimation, that directly learns the InSAR data distribution. GenInSAR's unsupervised training on satellite and simulated noisy InSAR images outperforms other five related methods in total residue reduction (over 16.5% better on average) with less over-smoothing/artefacts around branch cuts. GenInSAR's Phase, and Coherence Root-Mean-Squared-Error and Phase Cosine Error have average improvements of 0.54, 0.07, and 0.05 respectively compared to the related methods.