The coupled urbanization and eco-environment system is an important aspect of coupled human and natural systems. However, the time-space compression, long range interactions, and reconstruction of socio-economic structure at the global scale pose great challenges to the traditional analysis frameworks for human-nature systems. We are in urgent need of developing a brand new analysis framework. In this paper, based on the connotation of the coupled urbanization and eco-environment system and its four dimensions — space, time, appearance and organization, we propose a conceptual framework "Coupled Human and Natural Cube (CHNC)" to explain the coupling mechanism between urbanization and eco-environment, which is inspired by the theories including human-earth areal system, telecoupling, planetary urbanization, and perspectives from complexity science. We systematically introduce the concept, connotation, evolution rules and analysis dimensions of the CHNC. It is worth noting that there exist various "coupling lines" in the CHNC, which connects different systems and elements at multiple scales, and forms a nested, interconnected organic bigger system. The rotation of the CHNC represents the spatiotemporal nonlinear fluctuation of the urbanization and eco-environment system in different regions. As the system exchanges energy with the environment continually, the critical phase transition occurs when fluctuation reaches a certain threshold, and leads to emergence behaviors of the system. The CHNC has four dimensions — pericoupling and telecoupling, syncoupling and lagcoupling, apparent coupling and hidden coupling, intra-organization coupling and inter-organization coupling. We mainly focus on the theoretical connotation, research methods and typical cases of telecoupling, lagcoupling, hidden coupling, and inter-organization coupling, and finally put forward a human-nature coupling matrix to integrate multiple dimensions. In summary, the CHNC provides a more comprehensive and systematic research paradigm for understanding the evolution and coupling mechanism of the human-nature system, which expands the analysis dimension of coupled human and natural systems, and provides some scientific supports to formulate regional sustainable development policies for human wellbeing.