Dear jeichmann21,
You can also consider flying into CDG Paris Charles de Gaulle Airport which tends to be pretty economical from the US, especially from Chicago. Then you could take a later Meridiana flight out of CDG over to Napoli(NAP). Otherwise, you can stay overnight and take an economical 12:30pm EasyJet flight out of Paris Orly to Napoli. Also, if you fly in early enough into Paris, you can catch that 12:30pm flight out of Paris Orly to Napoli with EasyJet using the RER train or the AirFrance Bus (~€25 or so). During the Summer until mid-Sep or so, EasyJet runs 5pm flights out of Paris Orly to Napoli Capodichino(CAP):
http://www.easyjet.com/en/book/index.asp
http://www.meridiana.it/IG/pages/home_en.aspx
http://www.airfrance.com/double6/passage2.nsf/(LookupPublishedWeb)/en-EXCDG-CarsAF_ligne_HP?OpenDocument
As for Barcelona to Napoli, you could also consider using Alitalia, however, the company is in such bad shape these days, I can't recommend it. We used Alitalia from Roma to Valencia in May 2006 and paid around €195 for a round trip. Mirculously, we didn't hit any of Alitalia's notorious strikes or delays.
Buona Fortuna...