This paper introduces a novel pipeline to reconstruct the geometry of interacting multi-person in clothing on a globally coherent scene space from a single image. The main challenge arises from the occlusion: a part of a human body is not visible from a single view due to the occlusion by others or the self, which introduces missing geometry and physical implausibility (e.g., penetration). We overcome this challenge by utilizing two human priors for complete 3D geometry and surface contacts. For the geometry prior, an encoder learns to regress the image of a person with missing body parts to the latent vectors; a decoder decodes these vectors to produce 3D features of the associated geometry; and an implicit network combines these features with a surface normal map to reconstruct a complete and detailed 3D humans. For the contact prior, we develop an image-space contact detector that outputs a probability distribution of surface contacts between people in 3D. We use these priors to globally refine the body poses, enabling the penetration-free and accurate reconstruction of interacting multi-person in clothing on the scene space. The results demonstrate that our method is complete, globally coherent, and physically plausible compared to existing methods.