In recent years, heterogeneous graph convolutional networks have emerged as a mainstream approach for node classification due to their ability to effectively capture semantic information in heterogeneous networks. However, several challenges remain. Most existing studies focus on general heterogeneous networks, where only a single type of edge is assumed between any two nodes. This simplification overlooks the multiple relationships that exist among multi-type nodes in multiplex heterogeneous networks and fails to explicitly explore the impact of different relations on the representations of various node types. Moreover, the over-smoothing issue inherent in graph neural networks limits these models to capturing only low-order local information, making it difficult to learn global correlation patterns in the network. To address these challenges, this study proposes a multiplex heterogeneous graph neural network (MHGNN) designed for node classification. The proposed MHGNN first learns local initial representations of each node type under different relational contexts. It then explicitly models the importance of each relation and effectively integrates the representations of different node types across multiple relations, thus capturing the relational diversity within multiplex heterogeneous networks. In addition, drawing inspiration from the microeconomic concepts of substitutes and complements, the study constructs substitute and complement matrices that encode global similarity features. These matrices are incorporated into the model via graph neural aggregation to enhance the learning of higher-order global semantic information across different node types. Finally, contrastive learning is employed to reconcile and fuse the distinct yet complementary representations learned from both local and global views, yielding the final node embeddings. Extensive experiments conducted on six real-world datasets demonstrate that the proposed MHGNN significantly outperforms state-of-the-art models across various evaluation metrics for node classification.