Can FreePBX work inside a subdirectory? (re: reverse proxy)

I have an Apache web server that I use to create reverse proxies to several other private web servers.

For example:

http://public.webserver.com/tivo -> 192.168.0.1:8080

I’ve setup my Asterisk server (with FreePBX) like this:

http://public.webserver.com/pbx -> 192.168.0.1:80

…and it mostly works but FreePBX thinks it’s at the root of the webserver and not inside a subdirectory (i.e. “/pbx”) so certain links don’t work.

Is it possible to fix this or have this work like I’m describing?