This looks like a CSS or JavaScript clash between your page and Juicebox.
In order to determine the cause of the problem, try reverting to the default WordPress theme to see if this makes a difference.
If this does not help, try deactivating your plugins, one-by-one, until the problem disappears and you discover which plugin is causing the problem.
A workaround would be to embed the gallery in an <iframe> instead of using WP-Juicebox (which inserts the embedding code directly into your page).
(1) Create your Juicebox-Pro gallery with JuiceboxBuilder-Pro: http://www.juicebox.net/support/juiceboxbuilder/
(2) Upload your entire gallery folder (not just the contents) to your web server
(3) Enter the following code into the body of your post:
<iframe src="http://www.example.com/gallery_folder/index.html" width="800" height="600" frameborder="0" scrolling="no"></iframe>
... making sure that the 'src' attribute of the <iframe> points towards your the 'index.html' file inside your gallery folder.