Accurate user and item embedding learning is crucial for modern recommender systems. However, most existing recommendation techniques have thus far focused on modeling users' preferences over singular type of user-item interactions. Many practical recommendation scenarios involve multi-typed user interactive behaviors (e.g., page view, add-to-favorite and purchase), which presents unique challenges that cannot be handled by current recommendation solutions. In particular: i) complex inter-dependencies across different types of user behaviors; ii) the incorporation of knowledge-aware item relations into the multi-behavior recommendation framework; iii) dynamic characteristics of multi-typed user-item interactions. To tackle these challenges, this work proposes a Knowledge-Enhanced Hierarchical Graph Transformer Network (KHGT), to investigate multi-typed interactive patterns between users and items in recommender systems. Specifically, KHGT is build upon a graph-structured neural architecture to i) capture type-specific behavior semantics; ii) explicitly discriminate which types of user-item interactions are more important in assisting the forecasting task on the target behavior. Additionally, we further integrate the multi-modal graph attention layer with temporal encoding strategy, to empower the learned embeddings be reflective of both dedicated multiplex user-item and item-item collaborative relations, as well as the underlying interaction dynamics. Extensive experiments conducted on three real-world datasets show that KHGT consistently outperforms many state-of-the-art recommendation methods across various evaluation settings. Our implementation is available in https://github.com/akaxlh/KHGT.