The first Swiss national dietary survey (MenuCH) was used to screen disease burdens and greenhouse gas emissions (GHG) of Swiss diets (vegan, vegetarian, gluten-free, slimming), with a focus on gender and education level. The Health Nutritional Index (HENI), a novel disease burden-based nutritional index built on the Global Burden of Disease studies, was used to indicate healthiness using comparable, relative disease burden scores. Low whole grain consumption and high processed meat consumption are priority risk factors. Non-processed red meat and dairy make a nearly negligible contribution to disease burden scores, yet are key drivers of diet-related GHGs. Swiss diets, including vegetarian, ranged between 1.1–2.6 tons of CO2e/person/year, above the Swiss federal recommendation 0.6 ton CO2e/person/year for all consumption categories. This suggests that only changing food consumption practices will not suffice towards achieving carbon reduction targets: Systemic changes to food provisioning processes are also necessary. Finally, men with higher education had the highest dietary GHG emissions per gram of food, and the highest disease burden scores. Win–win policies to improve health and sustainability of Swiss diets would increase whole grain consumption for all, and decrease alcohol and processed meat consumption especially for men of higher education levels.