Science policy discourse often encourages interdisciplinary research as an approach that enhances the potential of science to produce breakthrough discoveries and solutions to real-world, complex problems. While there is a large body of research examining the relationship between interdisciplinarity and scientific discovery, there is comparatively limited evidence on and understanding of the connection between interdisciplinarity and the generation of scientific findings that address societal problems. Drawing on a large-scale survey, we investigate whether scientists who conduct interdisciplinary research are more likely to generate scientific findings with high societal visibility - that is, research findings that attract the attention of non-academic audiences, as measured by mentions to scientific articles in blogs, news media and policy documents. Our findings provide support for the idea that two facets of interdisciplinarity - variety and disparity - are associated positively with societal visibility. Our results show, also, that the interplay between these two facets of interdisciplinarity has a systematic positive and significant association with societal visibility, suggesting a reinforcing effect of spanning multiple and distant scientific fields. Finally, we find support for the contingent role of scientists' collaboration with non-academic actors, suggesting that the positive association between interdisciplinary research and societal visibility is particularly strong among scientists who collaborate with actors outside academia. We argue that this study provides useful insights for science policy oriented to fostering the scientific and societal relevance of publicly funded research.