Coronavirus Disease 2019 (COVID-19) became a pandemic around the world and has huge impacts on our economic and social systems, particularly on the healthcare system and the transportation and energy sectors. To examine a relationship between healthcare and energy sectors in the COVID-19 era, we propose a holistic application of Data Envelopment Analysis for Environmental Assessment (DEA-EA) to assess the COVID-19 response performance of 33 OECD (Organization for Economic Co-operation and Development) nations and investigate whether health insurance systems contribute to the performance. We also associate the performance with mobility, which is an energy consumption measure, to test the relationship through statistical analyses. In the DEA-EA, particularly, this study incorporates undesirable outputs (i.e., the number of confirmed cases and that of deaths) as well as desirable outputs (i.e., the number of total recovered people and that of total tested people) during April 2020 as the initial stage of COVID-19. While the former outputs need to be maximized, the latter ones need to be minimized in the assessment of healthcare system performance. This study finds that (a) the COVID-19 response performance of countries is varying and those with higher public health coverage have outperformed others with lower public coverage in terms of combating the COVID-19 outbreak, and (b) the healthcare system performance is significantly associated with mobility. Particularly, the second finding indicates that outperforming nations in the healthcare system are returning to the normal (with less volatility) while underperforming ones are still stagnating in terms of mobility. It implies that outperforming countries need to prepare for continuous commitment to clean/sustainable energy transition.