This really could apply to any theme but I've done this before and usually it works. With Twenty Twelve, it doesn't seem to work.
I'm doing this new theme built on Twenty Twelve and I'm using the hgroup to display a logo for the site and I want the main-navigation nav to appear beneath the logo and right now, it's in front of it. I've tried numerous z-index tricks in my CSS. Nothing seems to change.
The theme is here and if anyone has a suggestion to get the logo to appear over the nav, let me know.