Human Interaction Recognition (HIR) between two people in videos is a critical field in computer vision and pattern recognition, aimed at identifying and understanding human interaction and actions for applications such as healthcare, surveillance, and human-computer interaction. Despite its significance, video-based HIR faces challenges in achieving satisfactory performance due to the complexity of human actions, variations in motion, different viewpoints, and environmental factors. In the study, we proposed a two-stream deep learning-based HIR system to address these challenges and improve the accuracy and reliability of HIR systems. In the process, two streams extract hierarchical features based on the skeleton and RGB information, respectively. In the first stream, we utilised YOLOv8-Pose for human pose extraction, then extracted features with three stacked LSM modules and enhanced them with a dense layer that is considered the final feature of the first stream. In the second stream, we utilized SAM on the input videos, and after filtering the Segment Anything Model (SAM) feature, we employed integrated LSTM and GRU to extract the long-range dependency feature and then enhanced them with a dense layer that was considered the final feature for the 2nd stream module. Here, SAM is utilized for segmented mesh generation, and ImageNet for feature extraction from images or meshes, focusing on extracting relevant features from sequential image data. Moreover, we newly created a custom filter function to enhance computational efficiency to eliminate irrelevant key points and mesh components from the dataset. We concatenated the two stream features and produced the final feature that fed into the classification module. The extensive experiment with the benchmark dataset of the proposed model has 96.07\% accuracy. The high-performance accuracy of the proposed model proved its superiority.