Pixel-level classification for very high resolution (VHR) images is a crucial but challenging task in remote sensing. However, since the diverse ways of satellite image acquisition and the distinct structures of various regions, the distributions of the same semantic classes among different data sets are dissimilar. Therefore, the classification model trained on one data set (source domain) may collapse, when it is directly applied to another one (target domain). To solve this problem, many adversarial-based domain adaptation methods have been proposed. However, these methods only consider the source and the target domains independently in the adversarial training, where only the target domain is explicitly contributed to narrow the gap between the distributions of both domains. Unlike previous methods, we propose a triplet adversarial domain adaptation (TriADA) method that jointly considers both domains to learn a domain-invariant classifier by a novel domain similarity discriminator. Specifically, the discriminator takes a triplet of segmentation maps as input, where two segmentation maps from the same domain are to be distinguished from the two maps from the different domains during the adversarial learning. Consequently, it explicitly considers both domains' information to narrow the distribution gap across domains. To enhance the discriminability of the classifier on the target domain, a class-aware self-training strategy, which depends on the output of the discriminator, is proposed to assign pseudo-labels with high adapted confidence on target data to retrain the classifier. Extensive experiments on several VHR pixel-level classification benchmarks demonstrate the effectiveness of our method as well as its superiority to the-state of the art.