Understanding the interactions between humans and nature in the Anthropocene is central to the quest for both human wellbeing and global sustainability. However, the time-space compression, long range interactions, and reconstruction of socioeconomic structures at the global scale all pose great challenges to the traditional analytical frameworks of human-nature systems. In this paper, we extend the connotation of coupled human and natural systems (CHANS) and their four dimensions-space, time, appearance, and organization, and propose a novel framework: "Coupled Human and Natural Cube" (CHNC) to explain the coupling mechanism between humans and the natural environment. Our proposition is inspired by theories based on the human-earth areal system, telecoupling framework, planetary urbanization, and perspectives from complexity science. We systematically introduce the concept, connotation, evolution rules, and analytical dimensions of the CHNC. Notably there exist various "coupling lines" in the CHNC, connecting different systems and elements at multiple scales and forming a large, nested, interconnected, organic system. The rotation of the CHNC represents spatiotemporal nonlinear fluctuations in CHANS in different regions. As a system continually exchanges energy with the environment, a critical phase transition occurs when fluctuations reach a certain threshold, leading to emergent behavior of the system. The CHNC has four dimensions-pericoupling and telecoupling, syncoupling and lagcoupling, apparent coupling and hidden coupling, and intra-organization coupling and inter-organizational coupling. We mainly focus on the theoretical connotation, research methods, and typical cases of telecoupling, lagcoupling, hidden coupling, and inter-organizational coupling, and 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 analytical dimension of CHANS. The CHNC also provides a theoretical support for formulating regional, sustainable development policies for human wellbeing.