In your situation a number of solutions are possible, but neither of them includes Eurail Pass (for such trip it is a rip off and absolutely unnecessary):
1) If you want to simplify whole ticket thing as much as possible go with straight forward International ticket (TCV tariff) for the whole route Zuerich-Interlaken-Milano-Rome (will cost app. 100 euro per person). It works like a railway pass, but for certain route - you just get off train and hope in as many times as you like on your way. But be sure to specify exactly the route you want to use while purchasing it. Domestic Italian tickets like Rome-Civitavecchia, Pisa-Florence etc. cost quite cheap, so no need of any pass for Italy (check our Italy page for some ideas on types of trains and tariffs)
2) Unfortunately SBB canceled Promo e-tickets for domestic trips in Switzerland, so there is no easy way left to save some money (usual Half-fare card useful only if you travel a lot in Switzerland). So probably a good choice for you will be to purchase Swiss flexi pass for your domestic travels in Switzerland (flexi needed because of before and after Italy parts of your journey) -
http://www.swisstravelsystem.ch/index.php?id=131&L=1 I guess 4 days within one month will work good enough. In order to get from Switzerland to Italy cheaply you either use you pass till Swiss-Italy border + combine it with cheap domestic Italian tickets. Or look for SBB's Click and Rail offer (
https://www.sbb.ch/mct/wi/shop/b2c/adw.do?6056)
3) Another option is to use regular SBB domestic tickets for you Zuerich-Interlaken part and Swiss pass for your Swiss-Italian border -"3/11/09 Brig-Geneva-Bern-Geneva, 4/11/09 Geneva-Zurich." part. Because that second part of you Swiss journeys includes quite a lot of train ride, so pass will be probably the best option for it.