Remotely installing the OS itself probably isn't possible from off-subnet, as the EFI bootROM in your Mac probably doesn't have a way to find and connect to an Optical Disc Sharing server on another subnet; it probably expects to be able to find one locally via Bonjour or a simpler multicast- or broadcast-based discovery protocol, and it probably doesn't provide a UI for specifying an arbitrary IP address and port to connect to.
But if you just needed to mount a remote disc, you could do it, but it would take a little work.
- Have your housemate pop in the disc into the Windows box that has Apple's Optical Disc Sharing software installed.
- Have your housemate could run a tool like Bonjour Browser to look at what IP address and port is being advertised for the _odisk._tcp service on that Windows machine. Note that this port is selected dynamically, so you'll need to redo this step (and the next step) every time.
- You or your housemate would probably need to change the configuration of your home gateway to enable port forwarding between an external port of your home gateway and the internal IP address and port of the Optical Disc Sharing service on your home Windows box. You might be able to make things similar by making your home Windows box the "DMZ" (a.k.a. "Bastion Host", a.k.a. "Default Host") on your home network.
From your Mac at work, open Terminal and type:
hdiutil attach http://$HomeGWPubIPAddr:$PubPort/
...where $HomeGWPubIPAddr is the public IP address of your home gateway and $PubPort is the public port you defined in the port forwarding/mapping in step 3.