Understanding how online media frame issues is crucial due to their impact on public opinion. Research on framing using natural language processing techniques mainly focuses on specific content features in messages and neglects their narrative elements. Also, the distinction between framing in different sources remains an understudied problem. We address those issues and investigate how the framing of health-related topics, such as COVID-19 and other diseases, differs between conspiracy and mainstream websites. We incorporate narrative information into the framing analysis by introducing a novel frame extraction approach based on semantic graphs. We find that health-related narratives in conspiracy media are predominantly framed in terms of beliefs, while mainstream media tend to present them in terms of science. We hope our work offers new ways for a more nuanced frame analysis.