If the page is located on the same server you can use Server.Transfer, this will change the focus on the server to the new page without changing the address on the client.
If the page is located elsewhere I don't really know. You could use an full page iframe (although iframes are depricated technique) and load the website in this iframe. Then the client won't see the url in the addressbar (but the address will be visible in the source).
Why wouldn't you want to show the address to the client ? If it's for security reasons then your approach is just wrong.