Although humanoid robots are made to resemble humans, their stability is not yet comparable to ours. When facing external disturbances, humans efficiently and unconsciously combine a set of strategies to regain stability. This work deals with the problem of developing a robust hybrid stabilizer system for biped robots. The Linear Inverted Pendulum (LIP) and Divergent Component of Motion (DCM) concepts are used to formulate the biped locomotion and stabilization as an analytical control framework. On top of that, a neural network with symmetric partial data augmentation learns residuals to adjust the joint's position, and thus improving the robot's stability when facing external perturbations. The performance of the proposed framework was evaluated across a set of challenging simulation scenarios. The results show a considerable improvement over the baseline in recovering from large external forces. Moreover, the produced behaviors are human-like and robust to considerably noisy environments.