Can't connect to Jellyfin over HTTPS

I am running a Jellyfin server behind a reverse proxy, so clients connect to it via the address jellyfin.server.example.com on port 443 (the proxy takes care of SSL). I’ve got four devices (a Mac, an iPad, an iPhone, and an Apple TV) and this works on all of them except the Apple TV. Only if I allow non-SSL traffice on port 80 and give that as the port for Infuse does it work. Surely the Apple TV client is capable of HTTPS, right?