Research on a terrain-blind walking control that can walk stably on unknown and uneven terrain is an important research field for humanoid robots to achieve human-level walking abilities, and it is still a field that needs much improvement. This paper describes the design, implementation, and experimental results of a robust balance-control framework for the stable walking of a humanoid robot on unknown and uneven terrain. For robust balance-control against disturbances caused by uneven terrain, we propose a framework that combines a capture-point controller that modifies the control reference, and a balance controller that follows its control references in a cascading structure. The capture-point controller adjusts a zero-moment point reference to stabilize the perturbed capture-point from the disturbance, and the adjusted zero-moment point reference is utilized as a control reference for the balance controller, comprised of zero-moment point, leg length, and foot orientation controllers. By adjusting the zero-moment point reference according to the disturbance, our zero-moment point controller guarantees robust zero-moment point control performance in uneven terrain, unlike previous zero-moment point controllers. In addition, for fast posture stabilization in uneven terrain, we applied a proportional-derivative admittance controller to the leg length and foot orientation controllers to rapidly adapt these parts of the robot to uneven terrain without vibration. Furthermore, to activate position or force control depending on the gait phase of a robot, we applied gain scheduling to the leg length and foot orientation controllers, which simplifies their implementation. The effectiveness of the proposed control framework was verified by stable walking performance on various uneven terrains, such as slopes, stone fields, and lawns.