We present an over-segmentation based, dense stereo algorithm that jointly estimates segmentation and depth. For mixed pixels on segment boundaries, the algorithm computes foreground opacity (alpha), as well as color and depth for the foreground and background. We model the scene as a collection of fronto-parallel planar segments in a reference view, and use a generative model for image formation that handles mixed pixels at segment boundaries. Our method iteratively updates the segmentation based on color, depth and shape constraints using MAP estimation. Given a segmentation, the depth estimates are updated using belief propagation. We show that our method is competitive with the state-of-the-art based on the new Middlebury stereo evaluation, and that it overcomes limitations of traditional segmentation based methods while properly handling mixed pixels. Z-keying results show the advantages of combining opacity and depth estimation.