Large-scale synthetic datasets are beneficial to stereo matching but usually introduce known domain bias. Although unsupervised image-to-image translation networks represented by CycleGAN show great potential in dealing with domain gap, it is non-trivial to generalize this method to stereo matching due to the problem of pixel distortion and stereo mismatch after translation. In this paper, we propose an end-to-end training framework with domain translation and stereo matching networks to tackle this challenge. First, joint optimization between domain translation and stereo matching networks in our end-to-end framework makes the former facilitate the latter one to the maximum extent. Second, this framework introduces two novel losses, i.e., bidirectional multi-scale feature re-projection loss and correlation consistency loss, to help translate all synthetic stereo images into realistic ones as well as maintain epipolar constraints. The effective combination of above two contributions leads to impressive stereo-consistent translation and disparity estimation accuracy. In addition, a mode seeking regularization term is added to endow the synthetic-to-real translation results with higher fine-grained diversity. Extensive experiments demonstrate the effectiveness of the proposed framework on bridging the synthetic-to-real domain gap on stereo matching.