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Domain shift between medical images from multicentres is still an open question for the community, which degrades the generalization performance of deep learning models. Generative adversarial network (GAN), which synthesize plausible images, is one of the potential solutions to address the problem. However, the existing GAN-based approaches are prone to fail at preserving image-objects in image-to-image (I2I) translation, which reduces their practicality on domain adaptation tasks. In this paper, we propose a novel GAN (namely MI$^2$GAN) to maintain image-contents during cross-domain I2I translation. Particularly, we disentangle the content features from domain information for both the source and translated images, and then maximize the mutual information between the disentangled content features to preserve the image-objects. The proposed MI$^2$GAN is evaluated on two tasks---polyp segmentation using colonoscopic images and the segmentation of optic disc and cup in fundus images. The experimental results demonstrate that the proposed MI$^2$GAN can not only generate elegant translated images, but also significantly improve the generalization performance of widely used deep learning networks (e.g., U-Net).