In our fractional stereo matching problem, a foreground object with a fractional boundary is blended with a background scene using unknown transparencies. Due to the spatially varying disparities in different layers, one foreground pixel may be blended with different background pixels in stereo images, making the color constancy commonly assumed in traditional stereo matching not hold any more. To tackle this problem, in this paper, we introduce a probabilistic framework constraining the matching of pixel colors, disparities, and alpha values in different layers, and propose an automatic optimization method to solve a Maximizing a Posterior (MAP) problem using Expectation-Maximization (EM), given only a short-baseline stereo input image pair. Our method encodes the effect of background occlusion by layer blending without requiring a special detection process. The alpha computation process in our unified framework can be regarded as a new approach by natural image matting, which handles appropriately the situation when the background color is similar to that of the foreground object. We demonstrate the efficacy of our method by experimenting with challenging stereo images and making comparisons with state-of-the-art methods.