In this study, we aim to propose a novel method for quantifying and modeling the characteristics of non-verbal interactions between parents and children by leveraging advanced image recognition technologies, specifically through facial detection and expression recognition. This research focuses on non-verbal communication modalities-such as facial expressions and gaze-which play a critical role in the early developmental stages of infants. By analyzing the bidirectional emotional fluctuations and behavioral influences that occur between parents and children, the study seeks to clarify the underlying dynamics of their interactions. To achieve this, facial expression data from both parents and children are collected and analyzed with high accuracy. Subsequently, using a Hidden Markov Model (HMM), the temporal transitions inherent in non-verbal communication patterns are examined and systematically modeled. Through this system, we aim to capture and interpret both the psychological state of the parent and the emotional changes in the child. Based on this information, the ultimate goal is to develop a new type of support technology that contributes to enhancing the quality of parent-child relationships.