Animals possess a remarkable ability to navigate challenging terrains, achieved through the interplay of various pathways between the brain, central pattern generators (CPGs) in the spinal cord, and musculoskeletal system. Traditional bioinspired control frameworks often rely on a singular control policy that models both higher (supraspinal) and spinal cord functions. In this work, we build upon our previous research by introducing two distinct neural networks: one tasked with modulating the frequency and amplitude of CPGs to generate the basic locomotor rhythm (referred to as the spinal policy), and the other responsible for receiving environmental perception data and directly modulating the rhythmic output from the spinal policy to execute precise movements on challenging terrains (referred to as the descending modulation policy). This division of labor more closely mimics the hierarchical locomotor control systems observed in legged animals, thereby enhancing the robot's ability to navigate various uneven surfaces, including steps, high obstacles, and terrains with gaps. Additionally, we investigate the impact of sensorimotor delays within our framework, validating several biological assumptions about animal locomotion systems. Specifically, we demonstrate that spinal circuits play a crucial role in generating the basic locomotor rhythm, while descending pathways are essential for enabling appropriate gait modifications to accommodate uneven terrain. Notably, our findings also reveal that the multi-layered control inherent in animals exhibits remarkable robustness against sensorimotor delays. These findings advance our understanding of the fundamental principles governing the interplay between spinal and supraspinal mechanisms in biological locomotion. Moreover, they inform the design of bioinspired locomotion controllers that emulate these biological structures, facilitating natural movement in complex and realistic environments.