Global Mapping

We are running several instances of CF within our environment, and they all live within their own directory on the web server root. I am trying to create a /global-resources/ directory, also on the main website root, that will be accessible by all of them. I have created the directory and files, added a CF mapping, and set up a virtual directory mapping. The CF mapping is working correctly - I can include a .cfm file from the /global-resources/ directory without any problems. However, when I try to use the virtual directory mapping to call CSS and JS files, I am getting back 404 errors. Looking at the browser console, it is looking for the files inside the individual application I am in, rather than on the web root. Is it possible to do what I'm talking about? Any help would be appreciated, thanks!