This work aims to combine machine learning and control approaches for legged robots, and developed a hybrid framework to achieve new capabilities of balancing against external perturbations. The framework embeds a kernel which is a fully parametric closed-loop gait generator based on analytical control. On top of that, a neural network with symmetric partial data augmentation learns to automatically adjust the parameters for the gait kernel and to generate compensatory actions for all joints as the residual dynamics, thus significantly augmenting the stability under unexpected perturbations. The performance of the proposed framework was evaluated across a set of challenging simulated scenarios. The results showed considerable improvements compared to the baseline in recovering from large external forces. Moreover, the produced behaviours are more natural, human-like and robust against noisy sensing.