No you can use a Eurail Global Pass this pass is valid in both countries Switzerland and Italy and 29 countries more :D

A Swiss Railpass is valid just in Switzerland. There are different offers the
Eurail Swisspass (One Countrypass) or the SwissTravelpass (a own offer of Swiss Transportataion) the are some differences
the Swiss Travelpass includes almost 100% of public transport in Switzerland this includes Buses (Postauto),Trams,Ships (for example Steam Ships on Lake Lucerene or Lac Leman) and ofcourse a lot Raillines and more discounts on the mountainrails.

The Eurail Globalpass and Eurail Swisspass covers mostly just train lines across Switzerland and only limited bus services and few Ship ride (Lake Thun, Lake Brienz). 

The question is what you wanna do in Switzerland :)

It can be better to combine a Swiss Travelpass with cheap advance fares for the Italianpart
or you use a Eurail Globalpass (attention for Italian Highspeed services you need a reservation on top of the pass price is 10€ per seat )

IF you are wiling to sacrifice time for much lower price- in IT there are also 3-4 day passes for ONLY the local/regional trains from TrenItalia.

EUrail is for at least 4 days, so for just 2 (additional) trips it does not make sense. For more extensive travel In Swiss their own pass (can also buy just on the spot f.e. at Züri airport counter) is far better value. It also includes entry to many museums.

The Swiss Travel Pass includes almost all public transport in Switzerland and it also includes the entry to many museums.

If you are travelling with children, children travel for free until the day before their 16th birthday if the parent has a Swiss Travel Pass  (or another ticket from the Swiss Travel System) and an additional Swiss Family Card.  

https://www.sbb.ch/en/leisure-holidays/inspiration/international-guests/swiss-travel-pass.html