The goal of this paper is to enhance understanding of how bodily actions between two social partners are coordinated in interpersonal interactions in naturalistic contexts. We introduce information-theoretic measures as a new approach to capturing sensorimotor dynamics in child-parent social interaction. In particular, information flows were measured based on a set of variables extracted from multimodal fine-grained behavioral data in social interactions wherein a child and a parent played with novel toys. Our results showed that information-theoretic measures can indeed capture the inherent structure of perception and action dynamics and further information exchange patterns can be used to predict successful learning through child-parent interactions. Moreover, those information flows between sensorimotor variables reveal a set of underlying perceptual and motor patterns with cognitively plausible explanations. In summary, the present study represents the first steps to connect information-theoretic measures as a mathematically rigorous framework with embodied human communication and cognition.