Yes, the TIM (not Tim's) SIM card has some calling minutes to call US numbers for free. (No texting though as I understand it.)
But you can also just install the Google Voice app to let you do the same thing, for free, even to landlines. You can try Google Voice now before you leave for Italy. If you have a landline, try dialing it from within Google Voice. You can send/receive texts with Google Voice also. You will get a new US phone number (doesn't replace your old one) when you sign up for Google Voice. When you send a text from Google voice, your Google number is used for the text - that's what the person you send a text to receives, not your AT&T number.
When you are in Italy, be sure to add a +1 (international access code plus the US country code) to the front of any US number to dial it. You get a + by holding down the 0 on the dial pad.