Carbon emissions in the process of urbanization are usually analyzed using industry, population, and economic factors. It is a high demand to consider the coupling space-time change of "human-land-carbon". In addition, the land can also serve as an important factor of production, leading to great impacts on carbon emissions. This study aims to explore the interaction mechanism among urbanization, carbon emission, and the " production-living-ecological " space. The spatial structure of the DNA model was first selected. The three-level structure was then taken as the theoretical basis. The spatial coupling model of urbanization, carbon emission, and "production-living-ecological" space was finally established using the environmental Kuznets curve and Logistic equation. The mechanism of interaction was also proposed similar to the molecular structure of DNA. Taking Henan Province of China as an example, the regression analysis was carried out to construct the curve of urbanization rate, carbon emission, and the curve of "production-living-ecological" spatial area change during 1980-2020. The Tapio decoupling coefficient and correlation test were used to analyze the quantitative relationship and correlation degree between carbon emission and the space area of "production-living-ecological". The quantitative relationship was verified for the environmental Kuznets curve between urbanization and carbon emission. The mechanism of action was also achieved among them. The results showed that: 1) Population and land urbanization induced the imbalance of ecological, production, and living space structure, leading to the quality of the ecological environment. There was a serious negative decoupling between urbanization development and carbon emission level. The spatial layout was coordinated to gradually shift from the serious negative to moderate coupling, particularly with the advancement of urbanization upgrading, production, life, and ecological space in the further suitable integration. The optimal coupling relationship can be expected for the "man, earth, and carbon". 2) The empirical results showed that there was a significant inverse U-shaped curve relationship between urbanization rate and carbon emissions. The decoupling state showed a strong stage, indicating the overall characteristics of "negative growth decoupling to strong decoupling, intermittent weak decoupling, and growth coupling". The carbon peak was predicted in 2026 and then entered the stage of carbon emission reduction. 3) The comprehensive analysis showed that the " production-living-ecological " space shared a trend of the orderly reduction of production space, steady expansion of living space, and stable development of ecological space. The correlation analysis showed that the contribution rate of production space to carbon emission increased, whereas, the contribution of living space to carbon emission decreased, and there was a stable contribution of ecological space to carbon emission. Therefore, the space layout should slow down the expansion of living space, and then increase the proportion of ecological space and carbon sink, finally reducing the carbon emissions generated by production space. The finding can provide quantitative reference and decision-making on regional urbanization and dual-carbon strategy.