The aim of this study was to assess the extent to which a sense of competence and beliefs about parental roles in mothers and fathers influence coparenting and child engagement in triadic interactions during the first 2 years of the child's life, after other influential variables such as marital satisfaction and postpartum depression have been controlled for. The sample constituted 69 mother–father–infant families, whose sense of competence, beliefs in parental roles, postpartum depression, and marital satisfaction were assessed in our laboratory at 3, 9, and 18 months with self‐reported questionnaires. Coparenting support and conflict and child engagement were assessed with the Lausanne Trilogue Play. Results show that (i) predictors of coparenting and child engagement are not the same at each time point; (ii) a sense of competence in mothers is positively linked with coparenting support, particularly at 3 months, whereas in fathers, it is negatively linked with support, particularly at 18 months; (iii) discrepancies between mothers and fathers in beliefs about the importance of the mother's role is the main predictor of coparenting conflict at 18 months; and (iv) paternal beliefs about the importance of the father's and mother's roles are the main predictor of child engagement at 18 months. Copyright © 2015 John Wiley & Sons, Ltd.