We present a novel global stereo model designed for view interpolation. Unlike existing stereo models which only output a disparity map, our model is able to output a 3D triangular mesh, which can be directly used for view interpolation. To this aim, we partition the input stereo images into 2D triangles with shared vertices. Lifting the 2D triangulation to 3D naturally generates a corresponding mesh. A technical difficulty is to properly split vertices to multiple copies when they appear at depth discontinuous boundaries. To deal with this problem, we formulate our objective as a two-layer MRF, with the upper layer modeling the splitting properties of the vertices and the lower layer optimizing a region-based stereo matching. Experiments on the Middlebury and the Herodion datasets demonstrate that our model is able to synthesize visually coherent new view angles with high PSNR, as well as outputting high quality disparity maps which rank at the first place on the new challenging high resolution Middlebury 3.0 benchmark.