Sharing a video, seeing the attendees, and recording - at the same time?

Hi Zoom experts! I'd like to record a Zoom call during which I'll share a 10 minute video. I'd like the recording to show the faces of the attendees (only 2 + me, the host). Is this possible? When I've previously tried this, I only see the video, without the attendees faces in the corners.
Thanks so much for any suggestions!