When I shrink the window size down, the menu disappears totally behind the slider. I tried adding Z-index rules, changed position to relative, even tried absolute (all using Firebug) and I can’t figure out a fix for you.
I wonder if this has something to do with your slider. If it were me, I’d try the Genesis Reponsive slider and see if that displays the same. Each of your images would then have to be featured images on posts of a designated category, but I find that slider would easily handle what your current slider does for you.