This paper presents a computational approach to measuring information transfer in infant-caregiver interaction. It is supposed that both an infant and a caregiver mutually shape the interaction by sending various signals to each other, of which the dynamic structure changes according to the infant's age. We investigated such developmental change both in infants and caregivers by measuring transfer entropy within and between their body movements. Our analysis demonstrated that infants significantly improve their body coordination and social contingency between 6 to 13 months of age. Their gaze, for example, start responding to caregivers' gaze, which indicates the development of joint attention. The coordination between infants' two hands also drastically improves as they grow. Of particular interest is that such development in infants elicits caregivers' adaptation. Caregivers change their social responses and body coordination to a more sophisticated manner in order to further facilitate infant development. Our approach is the first study to quantitatively verify the "co-development" of infants and caregivers, which appears as increases in information transfer within and between their behaviors.