Videoconference conversations about data often entail screen sharing visualization artifacts, in which nonverbal communication goes largely ignored. Beyond presentation use cases, conversations supported by visualization also arise in collaborative decision making, technical interviews, and tutoring: use cases that benefit from participants being able to see one another as they exchange questions about the data. In this paper, we employ a reciprocal compositing of visualization and interface widgets over the mirrored video of one’s conversation partner, suggestive of a pane of glass, in which both parties can simultaneously manipulate composited elements via bimanual gestures. We demonstrate our approach with implementations of several visualization interfaces spanning the aforementioned use cases, and we evaluate our approach in a study (N = 16) comparing it to videoconferencing while using a mouse to interact with a collaborative web application. Our findings suggest that our approach promotes feelings of presence and mutual awareness of analytical intent.