Networks have been widely used to represent the relations between objects such as academic networks and social networks, and learning embedding for networks has thus garnered plenty of research attention. Self-supervised network representation learning aims at extracting node embedding without external supervision. Recently, maximizing the mutual information between the local node embedding and the global summary (e.g. Deep Graph Infomax, or DGI for short) has shown promising results on many downstream tasks such as node classification. However, there are two major limitations of DGI. Firstly, DGI merely considers the extrinsic supervision signal (i.e., the mutual information between node embedding and global summary) while ignores the intrinsic signal (i.e., the mutual dependence between node embedding and node attributes). Secondly, nodes in a real-world network are usually connected by multiple edges with different relations, while DGI does not fully explore the various relations among nodes. To address the above-mentioned problems, we propose a novel framework, called High-order Deep Multiplex Infomax (HDMI), for learning node embedding on multiplex networks in a self-supervised way. To be more specific, we first design a joint supervision signal containing both extrinsic and intrinsic mutual information by high-order mutual information, and we propose a High-order Deep Infomax (HDI) to optimize the proposed supervision signal. Then we propose an attention based fusion module to combine node embedding from different layers of the multiplex network. Finally, we evaluate the proposed HDMI on various downstream tasks such as unsupervised clustering and supervised classification. The experimental results show that HDMI achieves state-of-the-art performance on these tasks.