Real-world networks usually have a property of node heterophily, that is, the connected nodes usually have different features or different labels. This heterophily issue has been extensively studied in homogeneous graphs but remains under-explored in heterogeneous graphs, where there are multiple types of nodes and edges. Capturing node heterophily in heterogeneous graphs is very challenging since both node/edge heterogeneity and node heterophily should be carefully taken into consideration. Existing methods typically convert heterogeneous graphs into homogeneous ones to learn node heterophily, which will inevitably lose the potential heterophily conveyed by heterogeneous relations. To bridge this gap, we propose Relation-Aware Separation of Homophily and Heterophily (RASH), a novel contrastive learning framework that explicitly models high-order semantics of heterogeneous interactions and adaptively separates homophilic and heterophilic patterns. Particularly, RASH introduces dual heterogeneous hypergraphs to encode multi-relational bipartite subgraphs and dynamically constructs homophilic graphs and heterophilic graphs based on relation importance. A multi-relation contrastive loss is designed to align heterogeneous and homophilic/heterophilic views by maximizing mutual information. In this way, RASH simultaneously resolves the challenges of heterogeneity and heterophily in heterogeneous graphs. Extensive experiments on benchmark datasets demonstrate the effectiveness of RASH across various downstream tasks. The code is available at: https://github.com/zhengziyu77/RASH.