The IP address that you have bought or leased from the ISP is currently being assigned to your router's WAN interface as its own IP address so that all traffic from your LAN can be Port Address Translated through that single IP address. So that public IP no longer refers to just your machine itself, but to your entire network since you are effectively sharing the services provided through that single IP address to your entire network. When you specify the port with ":80" you are actually pointing towards the web (Port 80) interface of your own router which is accessed through its interfaces, WAN in this case.
What you need to do is configure a DNS server in your network which will route any lookup for a query to your site's url to the local IP address of the webserver on your LAN on which the site resides. For eg: if your DNS Server is on 192.168.1.15 and the Webserver on which your site is, is on 192.168.1.30, then create a DNS entry routing traffic destined to your website URL to 192.168.1.30 where the IES will direct it to the site on its drive.
Hope that answers your query.