Humanoid robots have shown success in locomotion and manipulation. Despite these basic abilities, humanoids are still required to quickly understand human instructions and react based on human interaction signals to become valuable assistants in human daily life. Unfortunately, most existing works only focus on multi-stage interactions, treating each task separately, and neglecting real-time feedback. In this work, we aim to empower humanoid robots with real-time reaction abilities to achieve various tasks, allowing human to interrupt robots at any time, and making robots respond to humans immediately. To support such abilities, we propose a general humanoid-human-object interaction framework, named RHINO, i.e., Real-time Humanoid-human Interaction and Object manipulation. RHINO provides a unified view of reactive motion, instruction-based manipulation, and safety concerns, over multiple human signal modalities, such as languages, images, and motions. RHINO is a hierarchical learning framework, enabling humanoids to learn reaction skills from human-human-object demonstrations and teleoperation data. In particular, it decouples the interaction process into two levels: 1) a high-level planner inferring human intentions from real-time human behaviors; and 2) a low-level controller achieving reactive motion behaviors and object manipulation skills based on the predicted intentions. We evaluate the proposed framework on a real humanoid robot and demonstrate its effectiveness, flexibility, and safety in various scenarios.