The backgrounds are working fine, and the HTML5 doesn’t really have anything to do with it. If it’s not working it’s due to your custom css….and you’ve made a lot of customizations so we’d have to see which part is affecting what.
I just slightly resized my browser and now I’m confused as to what your site is supposed to actually look like. I took 3 screenshots to show what everything looks like on my end –
Which one of these is it supposed to look like?
I create awesome sites for awesome people! Contact me if interested – firstname.lastname@example.org