The current landscape of binary code summarization predominantly revolves around the generation of a single summarization, limiting the scope of understanding and usability for reverse engineers. The existing approaches often fail to address the multifaceted needs of users, such as detailed insights into usage patterns, implementation nuances, and design rationale, as highlighted in the domain of source code summarization. Consequently, the necessity of multi-intent binary code summarization, an essential way to enhance the efficacy of reverse engineering processes, is underscored. To address this gap, our basic observation is that the two types of information essential for binary code summarization (i.e., the assembly code and pseudo code) can complement each other well. Specifically, the assembly code, characterized by its low-level nature, intricately delineates the execution logic, whereas the pseudo code, operating at a higher level, retains valuable contextual information. Based on this insight, we propose MiSum, a novel multi-modality heterogeneous code graph alignment and learning method to integrate information from both assembly code and pseudo code. MiSum introduces a unified multi-modality heterogeneous code graph (MM-HCG) that achieves alignment between assembly code graph and pseudo code graph and carries low-level execution details and high-level structural information. To fuse the graph information, we propose MM-HCG heterogeneous graph learning with heterogeneous mutual attention and message passing, which caters to important code blocks and discovers inter-dependencies between different forms of codes. We also propose an intent-aware summary generator with an intent-aware attention mechanism to produce customized summaries corresponding to multiple intents. Extensive experiments, including evaluations across various architectures and optimization levels, demonstrate that MiSum outperforms state-of-the-art baselines in BLEU, METEOR, and ROUGE-L metrics. Human evaluations further validate its ability to effectively support reverse engineers in understanding diverse binary code intents, providing a significant advancement in the field of binary code analysis.