Humanoid locomotion is a challenging task due to its inherent complexity and high-dimensional dynamics, as well as the need to adapt to diverse and unpredictable environments. In this work, we introduce a novel learning framework for effectively training a humanoid locomotion policy that imitates the behavior of a model-based controller while extending its capabilities to handle more complex locomotion tasks, such as more challenging terrain and higher velocity commands. Our framework consists of three key components: pre-training through imitation of the model-based controller, fine-tuning via reinforcement learning, and model-assumption-based regularization (MAR) during fine-tuning. In particular, MAR aligns the policy with actions from the model-based controller only in states where the model assumption holds to prevent catastrophic forgetting. We evaluate the proposed framework through comprehensive simulation tests and hardware experiments on a full-size humanoid robot, Digit, demonstrating a forward speed of 1.5 m/s and robust locomotion across diverse terrains, including slippery, sloped, uneven, and sandy terrains.