We consider scenarios in which we wish to perform joint scene understanding, object tracking, activity recognition, and other tasks in environments in which multiple people are wearing body-worn cameras while a third-person static camera also captures the scene. To do this, we need to establish person-level correspondences across first- and third-person videos, which is challenging because the camera wearer is not visible from his/her own egocentric video, preventing the use of direct feature matching. In this paper, we propose a new semi-Siamese Convolutional Neural Network architecture to address this novel challenge. We formulate the problem as learning a joint embedding space for first- and third-person videos that considers both spatial- and motion-domain cues. A new triplet loss function is designed to minimize the distance between correct first- and third-person matches while maximizing the distance between incorrect ones. This end-to-end approach performs significantly better than several baselines, in part by learning the first- and third-person features optimized for matching jointly with the distance measure itself.