Actually it's more like this: Your PC tells the other PC you want to send a file, and which port the other PC needs to use to get through to you. Then the other PC tries to connect to you on that port.

You need to figure out how to forward ports on your router, then you can go to mIRC options -> connect -> advanced and set the port range for DCC connections to the same range that you set in your router. You don't need to forward a lot of ports, a 4-5 should do. Any port above um, 1024 whatever it is will do, I personally use 5000-5010.