I thought at first that it must be the png images which often give transparency problems in IE but I didn't download them and the main text still showed through the background colors of the fly-out menu so it must be a problem with the menu code.
It's a common function of these menus. I have one where the drop down menus were not "disappearing" or being transparent in IE7, but when I added some text in the containing div, the drop down or fly-out menus that would have occupied the same space did not show at all. When I limited the width of the text <p> tag, the nearest drop down menus did not show but those further away did show, so obviously any text permanently occupying the space takes priority. Z-index does not seem to work.
I don't know what to suggest at the moment except to look for a menu that does not have this effect. Try
http://www.cssplay.co.uk/menus/index.html
perhaps this one:-
http://www.cssplay.co.uk/menus/slide_definition.html
which does not extend to the side.
Code downloaded to my PC will be deleted in due course.
WIN7; IE9, Firefox, Opera, Chrome and Safari for Windows; screen resolution usually 1366*768.
Also IE6 on W98 with 800*600 and IE8 on Vista 1440*900.