I think if you add
.MainMenu_SubMenu td { z-index: 999; }
to your skin.css the submenus will render ok.
DNN modules gets a z-index 90X


Regarding the DDR menu look at the wiki pages
http://www.dotnetnuke.com/Resources/W...

I have another webserver running DNN5.6.3 - have a custom skin created. The skin uses drop down menu and works just fine on the DNN5.6.3 site. I used the same skin on my DNN6 installation. The problem with modules in the content area are in from of the dropdown menus are present when I use my custom skin in DNN6 as well as the defualt DNN6 skin DarkKnight.
I have tried changing the host settings to HTML4 legacy - as noted in a previous post, I also tried the other two options XHTML1 transitional and strict. No noticable effect.

I had tried adding in .dnn_dnnsolpartmenu_ctldnnsolpartmenu_spmsub { z-index:999 !important;} but this did not help. Turns out, in IE8, Tools, Compatibility Settings.
By default IE8 sets View Intranet Sites in compatility mode as checked or active. So everytime I viewed the site it was in compatibility mode, (since I am working with a site that is not published yet). I removed the check mark for "View Intranet Sites in compatibility mode" and now everything displays properly.