Objectives ESBL/AmpC-producing Enterobacteriaceae are an emerging public health concern. As households with preschool children may substantially contribute to the community burden of antimicrobial resistance, we determined the prevalence, risk factors and co-carriage of ESBL/AmpC-producing bacteria in preschool children and their parents. Methods From April 2013 to January 2015, each month 2000 preschool children were randomly selected from Dutch population registries. The parents were invited to complete an epidemiological questionnaire and to obtain and send a faecal sample from the selected child and from one parent. Samples were tested for ESBL/AmpC-producing bacteria. Logistic regression was used to identify risk factors for ESBL/AmpC carriage in children and parents, and findings were internally validated by bootstrapping. Results In total, 1016 families were included and ESBL/AmpC prevalence was 4.0% (95% CI 3.2%–5.0%); 3.5% (95% CI 2.5%–4.8%) in children and 4.5% (95% CI 3.4%–6.0%) in parents. Attending a daycare centre (DCC) was the only significant risk factor for children (OR 2.1, 95% CI 1.0–4.3). For parents, the only significant risk factor was having one or more children attending DCCs (OR 2.2, 95% CI 1.2–4.8). For parents of ESBL/AmpC-positive children the OR for ESBL/AmpC carriage was 19.7 (95% CI 9.2–42.4). Co-carriage of specific ESBL/AmpC genotypes in child and parent occurred more often than expected by chance (14.6% versus 1.1%, P < 0.001). Conclusions In this study, intestinal carriage with ESBL/AmpCs was detected in ∼4% of households with preschool children. DCC attendance was a risk factor in both children and parents and co-carriage of specific genotypes frequently occurred in child–parent pairs. These findings suggest household transmission or/and family-specific exposure to common sources of ESBL/AmpC-producing bacteria.