Unsupervised domain adaptation is to transfer knowledge from a well-annotated source domain and learn an accurate classifier for an unlabeled target domain, which is particularly useful in multimodal medical image processing. Currently available adaptation approaches strongly reduce the domain bias or inconsistency in the latent space, deteriorating inherent data structures. To appropriately leverage the reduction of the domain discrepancy and the maintenance of the intrinsic structure, this paper proposes a dual U-DenseTransformer generation domain adaptation framework to bridge the gap between source and target domains and achieve translation. Specifically, we create a DenseTransformer with multi-head attention embedded in U-shape network to establish a dual-generator strategy, which is further enhanced by a new hybrid loss function and an edge-aware mechanism that preserve inherent data structure consistent. We apply our proposed method to medical image segmentation, with the experimental results showing that it works more effective and stable than currently available approaches. Particularly, the dice similarity was improved from 79.3% to 82.8%, while the average symmetric surface distance was reduced from 2.5 to 1.9.