Characteristics of parent-child interaction (PCI) early in life have been associated with later development in the child. Twin studies can help to disentangle child contributions to parent-child interaction, for example, by assessing the influence of the child's genetics on his/her social environment, which includes parental behaviour. Infant twins from a community sample [354 monozygotic (MZ), 268 same-sex dizygotic (DZ)] were assessed in terms of PCI at age 5 months. We used the classical twin design to map the aetiology of several parent and child PCI scales and their covariation. We investigated the relations between PCI and later parent-rated child's social communication, language, and autistic traits at ages 2 and 3. Heritability was below 20% for all the included PCI traits. Unique (nonshared) environmental influences substantially overlapped across several PCI scales, suggesting that idiosyncrasies linked to each session shaped the scoring of several traits in a systematic way. Factor analysis revealed three uncorrelated latent factors, which were conceptualized as 'child negative affect', 'positive affective interaction', and 'parent's supportive strategies'. Parents who were rated highly on 'sensitive responsiveness' at 5 months tended to rate their offspring higher in terms of socio-communicative and language development and lower in terms of autistic traits in the second and third years of life. This study maps the phenotypic and aetiological structure of PCI in early infancy and supports the view that parents' sensitive responsiveness towards their infant is associated with later developmental gains in several domains. We did not find strong evidence of any so-called evocative genetic effects on parents' behaviour. We discuss the results considering the general challenge for lab-based observational PCI measures to capture the richness of parent-child interaction.