This study presents an emotion-aware navigation framework -- EmoBipedNav -- using deep reinforcement learning (DRL) for bipedal robots walking in socially interactive environments. The inherent locomotion constraints of bipedal robots challenge their safe maneuvering capabilities in dynamic environments. When combined with the intricacies of social environments, including pedestrian interactions and social cues, such as emotions, these challenges become even more pronounced. To address these coupled problems, we propose a two-stage pipeline that considers both bipedal locomotion constraints and complex social environments. Specifically, social navigation scenarios are represented using sequential LiDAR grid maps (LGMs), from which we extract latent features, including collision regions, emotion-related discomfort zones, social interactions, and the spatio-temporal dynamics of evolving environments. The extracted features are directly mapped to the actions of reduced-order models (ROMs) through a DRL architecture. Furthermore, the proposed framework incorporates full-order dynamics and locomotion constraints during training, effectively accounting for tracking errors and restrictions of the locomotion controller while planning the trajectory with ROMs. Comprehensive experiments demonstrate that our approach exceeds both model-based planners and DRL-based baselines. The hardware videos and open-source code are available at https://gatech-lidar.github.io/emobipednav.github.io/.