Many domain adaptation approaches rely on learning cross domain shared representations to transfer the knowledge learned in one domain to other domains. Traditional domain adaptation only considers adapting for one task. In this paper, we explore multi-task representation learning under the domain adaptation scenario. We propose a neural network framework that supports domain adaptation for multiple tasks simultaneously, and learns shared representations that better generalize for domain adaptation. We apply the proposed framework to domain adaptation for sequence tagging problems considering two tasks: Chinese word segmentation and named entity recognition. Experiments show that multi-task domain adaptation works better than disjoint domain adaptation for each task, and achieves the state-of-the-art results for both tasks in the social media domain.