In I.E. 8 I have noticed after installing that the Normal Naviation menu drop downs options are underneath the ShoutBox. (if installed after navigation)
As you can see here on DBTech, it's working perfectly fine with the default skin. Can you try with a default skin on your forum? If it works, then it's a skin issue.
I'm unable to replicate this issue on your forum using either of your two installed skins. The dropdowns appear in front of the Shoutbox exactly as intended.