Hello dartkun,
I experimented a bit on your Website using both FireFox 2.0 and Internet Explorer 6. The white bar does show on the former and not the latter, the same way you described.
I saved your homepage to my hard disk to tweak it a bit and see if I could find the cause of this problem. As far as I can see, your problem is due to the CSS rendering differences between the two browsers. More specifically, I believe it might be that you're using a CSS background image for your main layout table.
There are many solutions to this problem, but most will involve sacrificing parts of your layout. So the most unobtrusive solution I have right now is to dispense with the Table background image and make it a Body background image instead. This should leave everything else intact. And even if you see any overlapping, you can simply keep everything the way it is now, and just put everything that's inside your main table between <div> </div> tags and give it a higher z-index. I don't think you'll have to do that, though; the first method should work just fine.
Of course, this is mostly speculation on my part. Since I couldn't download the background images you use (since they're CSS images), I had to speculate rather than experiment.
I hope that suggestion works for you . Best of luck.