It has been increasingly recognized that effective human-AI co-creation requires more than prompts and results, but an environment with empowering structures that facilitate exploration, planning, iteration, as well as control and inspection of AI generation. Yet, a concrete design approach to such an environment has not been established. Our literature analysis highlights that compositional structures-which organize and visualize individual elements into meaningful wholes-are highly effective in granting creators control over the essential aspects of their content. However, efficiently aggregating and connecting these structures to support the full creation process remains challenging. Therefore, we propose a design approach of leveraging compositional structures as the substrates and infusing AI within and across these structures to enable a controlled and fluid creation process. We evaluate this approach through a case study of developing a video co-creation environment using this approach. User evaluation shows that such an environment allowed users to stay oriented in their creation activity, remain aware and in control of AI's generation, and enable flexible human-AI collaborative workflows.