We address the problem of accurate capture of interactive behaviors between two people in daily scenarios. Most previous works either only consider one person or solely focus on conversational gestures of two people, assuming the body orientation and/or position of each actor are constant or barely change over each interaction. In contrast, we propose to simultaneously model two people's activities, and target objective-driven, dynamic, and semantically consistent interactions which often span longer duration and cover bigger space. To this end, we capture a new multi-modal dataset dubbed InterAct, which is composed of 241 motion sequences where two people perform a realistic and coherent scenario for one minute or longer over a complete interaction. For each sequence, two actors are assigned different roles and emotion labels, and collaborate to finish one task or conduct a common interaction activity. The audios, body motions, and facial expressions of both persons are captured. InterAct contains diverse and complex motions of individuals and interesting and relatively long-term interaction patterns barely seen before. We also demonstrate a simple yet effective diffusion-based method that estimates interactive face expressions and body motions of two people from speech inputs. Our method regresses the body motions in a hierarchical manner, and we also propose a novel fine-tuning mechanism to improve the lip accuracy of facial expressions. To facilitate further research, the data and code is made available at https://hku-cg.github.io/interact/ .