Health is at the forefront of clean air and climate action. However, most existing studies of health impacts were based on additive single-exposure effects, which often oversimplify the relationships between atmospheric components and health outcomes. This review examines various atmospheric components' common sources and differential health effects, including greenhouse gases and major air pollutants such as fine particulate matter (PM2.5). It emphasizes the need for a comparative assessment of health impacts across various atmospheric components. We further highlight black carbon as an illustrative example, given its higher toxicity compared with other major PM2.5 components. By integrating the best available findings on the differential effects of particulate matter components with multiple gridded estimates of air pollution concentrations and population data, we conducted a risk assessment to quantify the health benefits of particulate matter reductions associated with China's clean air actions (2013-2020) and future climate mitigation scenarios (2020-2060). Our assessments indicate that, in regions or during periods where black carbon accounts for a higher proportion of exposure reduction relative to other PM2.5 components, reducing per-unit concentrations of PM2.5 can prevent more premature deaths. We propose a conceptual framework for a health-oriented strategy to enhance the effectiveness of clean air and climate initiatives.