Household-based interventions are the mainstay of public health policy against epidemic respiratory pathogens when vaccination is not available. Although the efficacy of these interventions has traditionally been measured by their ability to reduce the proportion of household contacts who exhibit symptoms [household secondary attack rate (hSAR)], this metric is difficult to interpret and makes only partial use of data collected by modern field studies. Here, we use Bayesian transmission model inference to analyze jointly both symptom reporting and viral shedding data from a three-armed study of influenza interventions. The reduction in hazard of infection in the increased hand hygiene intervention arm was 37.0% [8.3%, 57.8%], whereas the equivalent reduction in the other intervention arm was 27.2% [-0.46%, 52.3%] (increased hand hygiene and face masks). By imputing the presence and timing of unobserved infection, we estimated that only 61.7% [43.1%, 76.9%] of infections met the case criteria and were thus detected by the study design. An assessment of interventions using inferred infections produced more intuitively consistent attack rates when households were stratified by the speed of intervention, compared with the crude hSAR. Compared with adults, children were 2.29 [1.66, 3.23] times as infectious and 3.36 [2.31, 4.82] times as susceptible. The mean generation time was 3.39 d [3.06, 3.70]. Laboratory confirmation of infections by RT-PCR was only able to detect 79.6% [76.5%, 83.0%] of symptomatic infections, even at the peak of shedding. Our results highlight the potential use of robust inference with well-designed mechanistic transmission models to improve the design of intervention studies.