This paper introduces a novel multi-dimensional framework for developing and deploying AI-human systems, incorporating both technical and managerial design principles. The paper then applies the framework to four standard human-AI interaction patterns, including Human Out Of the Loop (HOOTL), Human On the Loop (HOTL), Human In the Loop (HITL), and Hybrid Intelligence (HI). The dimensions are used to succinctly describe the essential characteristics of each pattern, highlighting potential risks and benefits, such as end-user resistance, employee deskilling, value-misalignment and employee upskilling and business model reengineering. The framework provides a valuable tool for AI developers and managers to characterize their current solutions and optimize the integration of humans and machines in complex systems.