I believe you can give absolute or relative paths in an include() command.
include("/usr/you/www/private/page.php");
include("../private/page.php");
etc...
does it give you errors if you try to included a file in this password protected directory? I'm not sure how that would work out.
Another option might be to place the file outside of your web root, then use a relative path to include it. This way no one can access it through a web browser.
HTH
---John Holmes...