As full AI-based automation remains out of reach in most real-world applications, the focus has instead shifted to leveraging the strengths of both human and AI agents, creating effective collaborative systems. The rapid advances in this area have yielded increasingly more complex systems and frameworks, while the nuance of their characterization has gotten more vague. Similarly, the existing conceptual models no longer capture the elaborate processes of these systems nor describe the entire scope of their collaboration paradigms. In this paper, we propose a new unified set of dimensions through which to analyze and describe human-AI systems. Our conceptual model is centered around three high-level aspects - agency, interaction, and adaptation - and is developed through a multi-step process. Firstly, an initial design space is proposed by surveying the literature and consolidating existing definitions and conceptual frameworks. Secondly, this model is iteratively refined and validated by conducting semi-structured interviews with nine researchers in this field. Lastly, to illustrate the applicability of our design space, we utilize it to provide a structured description of selected human-AI systems.