Interactive Argument Pair Identification is an emerging research task for argument mining, with the goal of identifying whether two arguments are interactively related. However, existing methods solely focus on the interaction representation among arguments or between arguments and context, neglecting the interaction between their two representations and do not specifically investigate the distinctiveness in representations between positive and negative samples of argument pairs. In this paper, we propose a Contrastive-Enhanced and Multi-Scale Semantic-Aware Framework to solve this problem. We employ Multi-Scale Semantic-Aware module to facilitate semantic interactions among the context of arguments and the debating parties, which aims to comprehensively understand the complete argumentation process. Additionally, we utilize Contrastive-Enhanced module to minimize the distance for positive samples of arguments and maximize the distance for negative samples, which assists the model in better distinguishing the relationships between arguments. The experimental results show that our method achieves the SOTA performance on the benchmark dataset. Further analysis demonstrates the effectiveness of our proposed modules.