Effective vaccines protect individuals by not only reducing the susceptibility to infection, but also reducing the infectiousness of breakthrough infections in vaccinated cases. To disentangle the vaccine effectiveness against susceptibility to infection (VE_S) and vaccine effectiveness against infectiousness (VE_I), we took advantage of Danish national data comprising 24,693 households with a primary case of SARS-CoV-2 infection (Delta Variant of Concern, 2021) including 53,584 household contacts. In this setting, we estimated VE_S as 61% (95%-CI: 59-63), when the primary case was unvaccinated, and VE_I as 31% (95%-CI: 26-36), when the household contact was unvaccinated. Furthermore, unvaccinated secondary cases with an infection exhibited a three-fold higher viral load compared to fully vaccinated secondary cases with a breakthrough infection. Our results demonstrate that vaccinations reduce susceptibility to infection as well as infectiousness, which should be considered by policy makers when seeking to understand the public health impact of vaccination against transmission of SARS-CoV-2.