Multilayer networks are increasingly used to capture complex relationships in financial systems. In this paper, we employ a multilayer and temporal network framework to analyze dynamic connections among cross-listed stocks. Each network layer corresponds to a distinct market, and a rolling window approach tracks the temporal evolution of connections, particularly during market shocks. To compare the roles of cross-listed firms in the two markets, we design a centrality imbalance indicator. Community detection is used to reveal hidden structures based on this indicator. The analysis shows that stocks from the same firms exert different levels of influence, and the key stocks in both A-shares and H-shares always shift. The connections can be significantly enhanced during periods of financial stress. Notably, community detection results indicate that differences in cross-listed firms’ importance may be linked to how strongly the corresponding stocks are connected. This study extends the application of multilayer and temporal network models to financial markets, offering a systematic approach to analyze evolving market relationships and their implications for financial risk.