Understanding the relationships between items can improve the accuracy and interpretability of recommender systems. Among these relationships, the substitute and complement relationships attract the most attention in e-commerce platforms. The substitutable items are interchangeable and might be compared with each other before purchasing, while the complementary items are used in conjunction and are usually bought together with the query item. In this paper, we focus on two issues of inferring the substitutable and complementary items: 1) how to model their mutual influence to improve the performance of downstream tasks, 2) how to further discriminate them by considering the strength of relationship for different item pairs. We propose a novel multi-task learning framework named Enhanced Multi-Relationships Integration Graph Convolutional Network (EMRIGCN). We regard the relationship inference task as a link prediction task in heterogeneous graph with different types of edges between nodes (items). To model the mutual influence between substitute and complement, EMRIGCN adopts a two-level integration module, i.e., feature and structure integration, based on experts sharing mechanism during message passing. To obtain the strength of relationship for item pairs, we build an auxiliary loss function to further increase or decrease the distances between embeddings of items with weak or strong relation in latent space. Extensive experiments on both public and industrial datasets prove that EMRIGCN significantly outperforms the state-of-the-art solutions. We also conducted A/B tests on real world recommender systems of Meituan Maicai, an online supermarket platform in China, and obtained 15.3% improvement on VBR and 15.34% improvement on RPM.