Interferometric synthetic aperture radar (SAR) data provide reflectivity, interferometric phase, and coherence images, which are paramount to scene interpretation or low-level processing tasks such as segmentation and 3-D reconstruction. These images are estimated in practice from a Hermitian product on local windows. These windows lead to biases and resolution losses due to the local heterogeneity caused by edges and textures. This paper proposes a nonlocal approach for the joint estimation of the reflectivity, the interferometric phase, and the coherence images from an interferometric pair of coregistered single-look complex (SLC) SAR images. Nonlocal techniques are known to efficiently reduce noise while preserving structures by performing the weighted averaging of similar pixels. Two pixels are considered similar if the surrounding image patches are "resembling." Patch similarity is usually defined as the Euclidean distance between the vectors of graylevels. In this paper, a statistically grounded patch-similarity criterion suitable to SLC images is derived. A weighted maximum likelihood estimation of the SAR interferogram is then computed with weights derived in a data-driven way. Weights are defined from the intensity and interferometric phase and are iteratively refined based both on the similarity between noisy patches and on the similarity of patches from the previous estimate. The efficiency of this new interferogram construction technique is illustrated both qualitatively and quantitatively on synthetic and true data.