Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this multiplexity will lead to misleading results. On the other hand, there exists redundant information between different interaction patterns between nodes. Recent research reveals the analogy between the community structure and the hyperbolic coordinate. To learn each node's effective embedding representation while reducing the redundancy of multiplex network, we then propose a unified framework combing multiplex network hyperbolic embedding and multiplex community detection. The intuitive rationale is that high order node embedding approach is expected to alleviate the observed network's sparse and noisy structure which will benefit the community detection task. On the contrary, the improved community structure will also guide the node embedding task. To incorporate the common features between channels while preserving unique features, a random walk approach which traversing in latent multiplex hyperbolic space is proposed to detect the community across channels and bridge the connection between node embedding and community detection. The proposed framework is evaluated on several network tasks using different real world dataset. The results demonstrates that our framework is effective and efficiency compared with state-of-the-art approaches.