Julia,
There is no direct night train from Interlaken to Rome. Here's the best route:
Leave Interlaken Ost at 18:31, connect in Spiez, and arrive at Milano Centrale at 21:35. Take the E 833 night train from Milano Centrale to Roma Tiburtina, departing at 22:05 and arriving at 04:52.
See the timetables on the German rail site, www.bahn.de. Click on the drop-down flag menu for English. After you get summary timetables showing several departure times and routes, click on the arrow to the left of each departure time to see the connecting points.