Looking at your code, this is a very very VERY bloated theme. Seriously, there’s no reason a page that simple should take over 4 seconds to fully load.
In addition to the “way too many nested DIV’s” issue, areas above and below the header menu span the entire page, so you can’t actually change just that section of the header to white background.
From the looks of things, this theme creates its CSS dynamically on page load, so chances are it’s going to be a hassle to fix. I would really recommend you find a different theme that’s easier to CSS edit, because any time you want to change something that’s not in the “Theme Options” you’re going to run into issues.
I know this isn’t the answer you were hoping for, but you’ve kinda backed yourself into a corner with your theme choice.