Do you have Barry Green's DVX Book? If not, buy it now. NOW! If you do, go look up the answer to this question. I think you know Steve, so maybe ask him to borrow his copy?
Anyways, the reason it appears interlaced is due to the pulldown that Panasonic uses. Are you shooting 24p or 24pA? That's important.
Basically, since you're not shooting on film, you don't have real 24p. Instead, what Panasonic did was they created a way to write it onto tape. Your DVX records a mixture of full frames and interlaced frames, and when you import it into your timeline the editing program can pull out those interlaced frames, leaving you with 24p. It does this differently for 24p and 24pA, so its important that you set up the right timeline - a 24p timeline for 24p, and a 60i timeline for 24pA.
As for solutions? Mess with your settings in FCE and check your camera. What is your framerate? What timeline are you in? What are your export settings?
Buy that book, I'm serious.