There has long been controversy over the potential for asymptomatic cases of the influenza virus to have the capacity for onward transmission, but recognition of asymptomatic transmission of COVID-19 stimulates further research into this topic. Here, we develop a Bayesian methodology to analyze detailed data from a large cohort of 727 households and 2515 individuals in the 2009 pandemic influenza A(H1N1) outbreak in Hong Kong to characterize household transmission dynamics and to estimate the relative infectiousness of asymptomatic versus symptomatic influenza cases. The posterior probability that asymptomatic cases [36% of cases; 95% credible interval (CrI): 32%, 40%] are less infectious than symptomatic cases is 0.82, with estimated relative infectiousness 0.57 (95% CrI: 0.11, 1.54). More data are required to strengthen our understanding of the contribution of asymptomatic cases to the spread of influenza.