MOTIVATION: The microbes in human body play a crucial role in influencing the functions of drugs, as they can regulate the activities and toxicities of drugs. Most recent methods for predicting drug-microbe associations are based on graph learning. However, the relationships among multiple drugs and microbes are complex, diverse, and heterogeneous. Existing methods often fail to fully model the relationships. In addition, the attributes of drug-microbe pairs exhibit long-distance spatial correlations, which previous methods have not integrated effectively. RESULTS: We propose a new prediction method named DHDMP which is designed to encode the relationships among multiple drugs and microbes and integrate the attributes of various neighbor nodes along with the pairwise long-distance correlations. First, we construct a hypergraph with dynamic topology, where each hyperedge represents a specific relationship among multiple drug nodes and microbe nodes. Considering the heterogeneity of node attributes across different categories, we developed a node category-sensitive hypergraph convolution network to encode these diverse relationships. Second, we construct homogeneous graphs for drugs and microbes respectively, as well as drug-microbe heterogeneous graph, facilitating the integration of features from both homogeneous and heterogeneous neighbors of each target node. Third, we introduce a graph convolutional network with cross-graph feature propagation ability to transfer node features from homogeneous to heterogeneous graphs for enhanced neighbor feature representation learning. The propagation strategy aids in the deep fusion of features from both types of neighbors. Finally, we design spatial cross-attention to encode the attributes of drug-microbe pairs, revealing long-distance correlations among multiple pairwise attribute patches. The comprehensive comparison experiments showed our method outperformed state-of-the-art methods for drug-microbe association prediction. The ablation studies demonstrated the effectiveness of node category-sensitive hypergraph convolution network, graph convolutional network with cross-graph feature propagation, and spatial cross-attention. Case studies on three drugs further showed DHDMP's potential application in discovering the reliable candidate microbes for the interested drugs. AVAILABILITY AND IMPLEMENTATION: Source codes and supplementary materials are available at https://github.com/pingxuan-hlju/DHDMP.