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Capturing accurate 3D human pose in the wild would provide valuable data for training motion-generation and pose-estimation methods. While video-based estimation approaches have become increasingly accurate, they often fail in common scenarios involving self-contact, such as a hand touching the face. In contrast, wearable bioimpedance sensing can cheaply and unobtrusively measure ground-truth skin-to-skin contact. Consequently, we propose a novel framework that combines visual pose estimators with bioimpedance sensing to capture the 3D pose of people by taking self-contact into account. Our method, BioTUCH, initializes the pose using an off-the-shelf estimator and introduces contact-aware pose optimization during measured self-contact: reprojection error and deviations from the input estimate are minimized while enforcing vertex proximity constraints. We validate our approach using a new dataset of synchronized RGB video, bioimpedance measurements, and 3D motion capture. Testing with three input pose estimators, we demonstrate an average of 11.7% improvement in reconstruction accuracy. We also present a miniature wearable bioimpedance sensor that enables efficient large-scale collection of contact-aware training data for improving pose estimation and generation using BioTUCH. Code and data are available at biotuch.is.tue.mpg.de