This paper presents a control framework designed to enhance the stability and robustness of legged robots in the presence of uncertainties, including model uncertainties, external disturbances, and faults. The framework enables the full-state feedback estimator to estimate and compensate for uncertainties in the whole-body dynamics of the legged robots. First, we propose a novel moving horizon extended state observer (MH-ESO) to estimate uncertainties and mitigate noise in legged systems, which can be integrated into the framework for disturbance compensation. Second, we introduce a three-level whole-body disturbance rejection control framework (T-WB-DRC). Unlike the previous two-level approach, this three-level framework considers both the plan based on whole-body dynamics without uncertainties and the plan based on dynamics with uncertainties, significantly improving payload transportation, external disturbance rejection, and fault tolerance. Third, simulations of both humanoid and quadruped robots in the Gazebo simulator demonstrate the effectiveness and versatility of T-WB-DRC. Finally, extensive experimental trials on a quadruped robot validate the robustness and stability of the system when using T-WB-DRC under various disturbance conditions.