Infant attachment configurations with mothers and fathers: Implications for triadic interaction quality and children's parental preferences

•Configurations of infant-mother and infant-father attachment relationships at age 1 were related to triadic family interaction quality at age 3.•Families with two secure relationships (double secure) showed the highest quality triadic interactions, whereas discordant families (one secure and one insecure relationship) showed no better triadic interaction quality than double insecure families (two insecure relationships).•Children in discordant families showed stronger preferences for one parent over the other than children in double secure or double insecure families.•Stronger parental preferences were related to less cohesiveness and more detachment in triadic interactions, and mediated the link between attachment discordance and both variables.•Triadic (mother-father-child) interaction quality at age 3 appears to vary as a function of configurations of infants’ attachment patterns with both mother and father.