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For bike sharing systems, demand prediction is crucial to ensure the timely re-balancing of available bikes according to predicted demand. Existing methods for bike sharing demand prediction are mostly based on its own historical demand variation, essentially regarding it as a closed system and neglecting the interaction between different transportation modes. This is particularly important for bike sharing because it is often used to complement travel through other modes (e.g., public transit). Despite some recent progress, no existing method is capable of leveraging spatiotemporal information from multiple modes and explicitly considers the distribution discrepancy between them, which can easily lead to negative transfer. To address these challenges, this study proposes a domain-adversarial multi-relational graph neural network (DA-MRGNN) for bike sharing demand prediction with multimodal historical data as input. A temporal adversarial adaptation network is introduced to extract shareable features from demand patterns of different modes. To capture correlations between spatial units across modes, we adapt a multi-relational graph neural network (MRGNN) considering both cross-mode similarity and difference. In addition, an explainable GNN technique is developed to understand how our proposed model makes predictions. Extensive experiments are conducted using real-world bike sharing, subway and ride-hailing data from New York City. The results demonstrate the superior performance of our proposed approach compared to existing methods and the effectiveness of different model components.