A client is hosting their website on their own internal server which is also a proxy server

This is their current setup:

- The server hosts their web site under IIS with port 8080
- External requests to www.website.com (port 80) are translated to internal requests to the server (port 8080)
- Port number 8080 was chosen as this server is also a proxy server and port 80 is already in use – this cannot be changed
- Identified the below option in the web.config file:

<add key="MapAlternatePort" value="true"/>

Setting this value to true displays the website correctly within their Network while externally it shows with no styles

Setting this value to false has the opposite effect: internally it shows with no styles while externally it shows up fine.
 

Is there some way to work around this in the web.config? The client is adament that a second rule created on the router is not an option.