Understanding the risk of infection from household- and community-exposures and the transmissibility of asymptomatic infections is critical to SARS-CoV-2 control. Limited previous evidence is based primarily on virologic testing, which disproportionately misses mild and asymptomatic infections. Serologic measures are more likely to capture all previously infected individuals. We apply household transmission models to data from a cross-sectional, household-based population serosurvey of 4,534 people >/=5 years from 2,267 households enrolled April-June 2020 in Geneva, Switzerland. We found that the risk of infection from exposure to a single infected household member aged >/=5 years (17.3%,13.7-21.7) was more than three-times that of extra-household exposures over the first pandemic wave (5.1%,4.5-5.8). Young children had a lower risk of infection from household members. Working-age adults had the highest extra-household infection risk. Seropositive asymptomatic household members had 69.4% lower odds (95%CrI,31.8-88.8%) of infecting another household member compared to those reporting symptoms, accounting for 14.5% (95%CrI, 7.2-22.7%) of all household infections.