for your code you need to add z-index to the .submenu class:
.submenu {
border: 1px #ffffff solid;
padding: 0px;
background: #dee9f3;
margin-left: 0px;
margin-top: 2px;
z-index: 1000;
}
I found this by using the techniques here:
Troubleshooting DotNetNuke Skins