Parental mental health subclinical features, such as stress, anxiety, and depression, have been reported to significantly influence the dynamics of parent-infant interaction, which sets the stage for early attention, learning, and social communication development. However, less is known about the influence of cognitive and social features, such as those related to broad autism phenotype (BAP) traits, despite their documented impact on attention control and sensory processing. The present study examines how parental BAP traits may relate to parent-infant interaction by focusing on their behaviors, using head-mounted eye-tracking to provide objective measures. Results indicated that BAP traits were related to rates of parent sustained attention and object handling but did not predict infants’ sustained attention during the interaction. The findings of variability in parental play behaviors based on BAP traits raise important questions regarding the direct impact of parental characteristics on early social interaction, infants’ potential adaptations to their learning environments, and the significance of BAP traits in infant development.