From my friend Rob Rolsma‘s findings:
To display a DHTML over a Flash object the Flash object must have its window mode set to transparent. This is achieved by setting the “wmode” parameter for the object tag AND the embed tag.
Within the object element for the Flash object include the following element:
<param name="wmode" value="transparent" />
Within the embed element for the Flash object, include the following attribute:
wmode="transparent"