Achieving both behavioral similarity and behavioral appropriateness in human-like motion generation for humanoid robots remains an open challenge. This challenge is further compounded by the requirement of cross-embodiment adaptability. To address this problem, we propose HuBE, a morphology-aware framework for human-like behavior execution in humanoid robots. HuBE integrates robot state, goal pose, and situational context to generate behaviors that are both behaviorally similar and appropriate, while reducing structural mismatches between motion generation and execution. To support this framework, we construct HPose, a context-enriched dataset featuring fine-grained situational annotations. Furthermore, we introduce a bone-scaling-based data augmentation strategy that ensures millimeter-level compatibility across heterogeneous humanoid robots. Comprehensive evaluations on multiple commercial platforms demonstrate that HuBE significantly improves motion similarity, behavioral appropriateness, and computational efficiency over strong baselines. Overall, HuBE provides a transferable foundation for robust, human-like behavior execution across diverse humanoid robots.