<p><?tk 4?>The problem of disturbance rejection in humanoid robots has been properly studied, with most prior work focusing on hip-ankle-stepping compliance control strategies or whole-body inverse dynamics control. This paper presents an adaptive disturbance rejection balance controller based on a Variable-inertia Centroidal Model Predictive Control (ViC-MPC) approach, designed to address both minor disturbances that affect standing balance and major disturbances requiring stepping adjustments. The controller also facilitates reliable balance recovery after stepping adjustments. The humanoid robot is modeled as a spatial variable-inertia ellipsoid, representing the distribution of centroidal dynamics, with the contact wrenches optimized in real-time through a customized MPC formulation. Inspired by capturability-based constraints, we propose an adaptive dynamic stability transition strategy. This strategy is activated based on the Retrospective Horizon Average Centroidal Velocity (RHACV) and the Capture Point (CP), ensuring effective stepping adjustments and disturbance rejection. With the torque-controlled humanoid robot BHR8P, extensive simulation and experimental results demonstrate the effectiveness of the proposed method, highlighting its capability to adapt to and recover from various disturbances with improved stability.</p>