Here is the response I received from Tableau Support:
Thank you for contacting Tableau Technical Support. Based on attachment provided, I understand there is concern with the Tableau embedded view overlapping the ASP.NET popup menu.
Tableau Technical Support does not offer support for custom embedding. The Tableau Server embed code does not utilize any parameters to edit the layout or CSS of the webpage. However, I believe the issue can be resolved by modifying the CSS z-index property of the webpage to change the element stack order. Setting the stack order of the popup menu higher than the Tableau Server embed code should accomplish the desired result.
For more information on the CSS z-index property, please view the following: http://www.w3schools.com/cssref/pr_pos_z-index.asp
With this advice I proceded to add
to my menu css and that resolved the issue.