Hello Sandra,

an interail pass for Italy is valid in Italy. 

Basel is in Switzerland. You simply can’t go with an interrail pass that is only valid in Italy traveling in Switzerland. 

It’s as simple as that.

Thank you Hektor, this means I have to buy a Switzerland Pass, too - also I am “only” travelling through Switzerland?

no need to buy a switzerland pass you could just buy a single ticket from Basel to your first italian destination or to the first stop of the bordercrossing train in Italy.

But thsi will cost an arm+leg-swiss fares as fullare pretty high

IF you know the date in advance then try if you can get a lower prices sparpreis=fixed to that day/.train.

You should of course have looked closer at what you biught before.

Or you buy directly a Global Pass for hole Europe, than you can use also 2 days in your home country to get to leave and get back to your homecountry.