With the recent explosive increase of digital data, image recognition and retrieval become a critical practical application. Hashing is an effective solution to this problem, due to its low storage requirement and high query speed. However, most of past works focus on hashing in a single (source) domain. Thus, the learned hash function may not adapt well in a new (target) domain that has a large distributional difference with the source domain. In this paper, we explore an end-to-end domain adaptive learning framework that simultaneously and precisely generates discriminative hash codes and classifies target domain images. Our method encodes two domains images into a semantic common space, followed by two independent generative adversarial networks arming at crosswise reconstructing two domains' images, reducing domain disparity and improving alignment in the shared space. We evaluate our framework on {four} public benchmark datasets, all of which show that our method is superior to the other state-of-the-art methods on the tasks of object recognition and image retrieval.