Your live site appears to be working fine in Chrome, Firefox, IE and Safari with respect to the issue you described.
If you are experiencing the issue on your local staging site, the cause can be a number of reasons, including incorrect HTML or CSS formatting. If your HTML looks fine, I suggest having a look at the CSS zindex property. W3Schools provides a nice overview:
http://www.w3schools.com/cssref/pr_pos_z-index.asp
Note: I noticed that your HTML does not include a DOCTYPE, which can potentially make it harder to keep your site rendering consistently across different browsers, since it can trigger quirks mode.