"[Joe] is head over heels for [Ashley]," a source tells PEOPLE. "He thinks she is down-to-earth and absolutely beautiful. He hasn't been this into a girl in a long time."
The two haven't been dating long, but they're getting more serious: A source says Greene, 23, recently took Jonas home with her to meet the parents in Florida.
While Jonas, 21, and his Twilight star sweetheart lead busy lives, a source says that while the couple has a momentary break from work, "They want to spend as much time together as possible."
A rep for Jonas had no comment.