Faith, you can see this entire run on www.sbb.ch but you can only see Milan/Interlaken Ost on www.trenitalia.com (reason coming up).
Since you will most likely be purchasing your tickets in Italy, the Trenitalia screens do not show the private trains and gondolas from Interlaken into the Lauterbrunnen Valley. The reason that you can't see these systems on Trenitalia is that the Swiss want to be paid in Swiss Francs for these runs and you can't do that in Italy.
Not to worry. When you get to Italy, book your Milan/Interlaken Ost ticket. When you get to Interlaken Ost, you can buy your Interlaken Ost/Murren tickets there. They will accept Visa or Swiss Francs. Then, walk out to track 2A and take the 20 minute ride on the train into Lauterbrunnen. It's a very scenic ride along a river. It's not a cog train.
Now, how to get quick Swiss Francs. When you change trains at Spiez (and you will), simply run around to the other side of the train station and make a withdrawl from the ATM there. You get Swiss Francs in Switzerland.
Next, there are two ways to get to Murren. The Swiss train site will route you from Lauterbrunnen to Stechelberg on a bus from Lauterbrunnen (10 minutes) where you get the gondola to Gimmelwald and then at Gimmelwald, change to a gondola to Murren. The other way is to walk across the street from the Lauterbrunnen train station to Gondola up to Grutschalp where you transfer to a cog train for a short ride into Murren. Either way is fine. You will love the whole experience.