There is a trick in WebEasy Professional that will allow you to do this.
Solution
1) Add a new page at the end of your site.
2) Set the background audio on this page.
3) Go to the "Build" menu and select "Preview".
4) Click the "Options" button.
5) Check the "Dynamic HTML" box.
6) Click the "Advanced" button.
7) In the "Web Site Style" box select "Split with last page as frame".
8) Click OK.
9) Click OK again.
10) Click OK to preview your site.
The last page of your site will become a frame along one side of the screen. This frame will never change, so the audio will play continually. You can put links on this page to your other pages to create a "navigation bar" that will be always available regardless of which page of your site is being viewed.