Traversability prediction is a fundamental perception capability for autonomous navigation. Deep neural networks (DNNs) have been widely used to predict traversability during the last decade. The performance of DNNs is significantly boosted by exploiting a large amount of data. However, the diversity of data in different domains imposes significant gaps in the prediction performance. In this work, we make efforts to reduce the gaps by proposing a novel pseudo-trilateral adversarial model that adopts a coarse-to-fine alignment (CALI) to perform unsupervised domain adaptation (UDA). Our aim is to transfer the perception model with high data efficiency, eliminate the prohibitively expensive data labeling, and improve the generalization capability during the adaptation from easy-to-access source domains to various challenging target domains. Existing UDA methods usually adopt a bilateral zero-sum game structure. We prove that our CALI model -- a pseudo-trilateral game structure is advantageous over existing bilateral game structures. This proposed work bridges theoretical analyses and algorithm designs, leading to an efficient UDA model with easy and stable training. We further develop a variant of CALI -- Informed CALI (ICALI), which is inspired by the recent success of mixup data augmentation techniques and mixes informative regions based on the results of CALI. This mixture step provides an explicit bridging between the two domains and exposes underperforming classes more during training. We show the superiorities of our proposed models over multiple baselines in several challenging domain adaptation setups. To further validate the effectiveness of our proposed models, we then combine our perception model with a visual planner to build a navigation system and show the high reliability of our model in complex natural environments.