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The exploration of the dependency structure of the Chinese and EU carbon trading markets is crucial to the construction of a globally harmonized carbon market. In this paper, we studied the characteristics of structural interdependency between China's major carbon markets and the European Union (EU) carbon market before and after the launch of the national carbon emissions trading scheme (ETS) and the occurrence of the new coronavirus (COVID-19) by applying the C-vine copula method, with the carbon trading prices of the EU, Beijing, Shanghai, Guangdong, Shenzhen and Hubei as the research objects. The study shows that there exists a statistically significant dependence between the EU and the major carbon markets in China and their extremal dependences and dependence structures are different at different stages. After the launch of the national carbon ETS, China has become more independent in terms of interdependency with the EU carbon market, and is more relevant between domestic carbon markets. Most importantly, we found that the dependence between the EU and Chinese carbon markets has increased following the outbreak of COVID-19, and tail dependency structures existed before the launch of the national carbon ETS and during the outbreak of the COVID-19. The results of this study provide a basis for the understanding of the linkage characteristics of carbon trading prices between China and the EU at different stages, which in turn can help market regulators and investors to formulate investment decisions and policies. [ABSTRACT FROM AUTHOR]