The robust balancing capability of humanoids is essential for mobility in real environments. Many studies focus on implementing human-inspired ankle, hip, and stepping strategies to achieve human-level balance. In this paper, a robust balance control framework for humanoids is proposed. Firstly, a Model Predictive Control (MPC) framework is proposed for Capture Point (CP) tracking control, enabling the integration of ankle, hip, and stepping strategies within a single framework. Additionally, a variable weighting method is introduced that adjusts the weighting parameters of the Centroidal Angular Momentum damping control. Secondly, a hierarchical structure of the MPC and a stepping controller was proposed, allowing for the step time optimization. The robust balancing performance of the proposed method is validated through simulations and real robot experiments. Furthermore, a superior balancing performance is demonstrated compared to a state-of-the-art Quadratic Programming-based CP controller that employs the ankle, hip, and stepping strategies.