Is Joe jealous of Ashley's onscreen love?

Joe Jonas and Ashley Greene may seem more in love than ever, but it didn't take long for the rumor mill to start buzzing that Joe has been super jealous of Ashley's The Twilight Saga: Breaking Dawn onscreen husband, Jackson Rathbone. Since Ashley's role as Alice Cullen calls for her to kiss and flirt with Jackson while filming, it's hard to imagine Joe not getting a little jealous of his girlfriend as he watches from the sidelines. Although Jackson tells J-14 that Ashley is a "sweetheart," the two costars are strictly friends in real life. Joe has nothing to worry about!