Katie,
I've made that trip a number of times and it's very easy (although it will take most of a day for travel). You may have had issues with finding train information depending on which part of June you're searching. There will be a schedule change about 12 June, so schedules after that may not be posted yet.
It would help to know which of the five Cinque Terrre (note sp.) towns you'll be staying in? Also, where are you staying in the Berner Oberland?
I've found that it's often necessary to get an early start on that trip, so you might consider something like this (I used an arbitrary date of 15 May to check).....
Depart Monterosso at 07:29, arriving Lauterbrunnen at 14:55 (time 7H:26M, 4 changes in Levanto, Milano Centrale, Spiez and Interlaken Ost). There are numerous other solutions available, but most of them take longer or have more changes. The route suggested above is one of the shortest and easiest, and gets you to the destination at a decent time to check into your hotel and do a brief walkabout before dinner.