BACKGROUND: Low birthweight and preterm birth are associated with an increased risk of neonatal death and chronic conditions across the life course. Reducing these adverse birth outcomes is a global public health priority and requires strategies to improve health care during pregnancy. We aimed to assess the effect of a Swiss health policy expansion fully covering illness-related costs during pregnancy on health outcomes in newborn babies. METHODS: We implemented a quasi-experimental difference in regression discontinuity design to assess the effect of expansion of Swiss health insurance (on March 1, 2014), to fully cover health-care costs during pregnancy and 8 weeks postpartum, on neonatal outcomes. Before this reform, only costs specific to the standard monitoring of a normal pregnancy were covered. Babies born before March 1, 2014, and their mothers were assigned to the unexposed group, and babies born on or after March 1, 2014, and their mothers were assigned to the exposed group. We included nearly all children born 2011-19 in Switzerland within a period of 9 months around the date March 1, 2014, and control years 2012, 2016, and 2018. Outcomes were birthweight, low birthweight, very low birthweight, gestational age, preterm or extremely preterm birth, and neonatal death. We estimated the intention-to-treat effect of the policy using parametric regression models. FINDINGS: 61 910 children were born 9 months before and 63 991 were born 9 months after March 1, 2014. 382 861 children were born in the same time period around the three control dates. In the period before policy implementation, mean birthweight was 3289 g, gestational age was 275 days, and 6·5% of children had low birthweight, 1·0% very low birthweight, 7·1% were preterm, 0·4% were extremely preterm, and 0·3% died within the first 28 days of life. After initiation of the policy (vs before) mean birthweight increased by 23 g (95% CI 5 to 40) and the predicted proportion of low birthweight births decreased by 0·81% (0·14 to 1·48) and of very low birthweight births decreased by 0·41% (0·17 to 0·65). The effect on very low birthweight was not robust in sensitivity analyses. The policy had a negligible effect on gestational age (mean difference 1 day, 95% CI 0 to 1) and no clear effects on the other examined outcomes. The change in predicted proportion for preterm births was -0·39% (95% CI -1·2 to 0·38), for extremely preterm births was -0·09% (-0·27 to 0·08), and for neonatal death was -0·07% (-0·2 to 0·07). INTERPRETATION: Free access to prenatal care in Switzerland reduced the risk of some adverse health outcomes in newborn babies. Expanding health-care coverage is a relevant health system intervention to reduce the risk of adverse health outcomes in the newborn baby and, potentially, across the life course. FUNDING: Swiss National Science Foundation.