If the server is providing data to the webpage, it should be able to provide data to the Roku as well. You'll probably need the following bits to get this working.
1. Create a timer loop as jbrave mentioned above.
2. Query your server for the data that forms the webpage (XML/images are likely preferred format).
3. Parse the data from the server and render it using BrightScript tools.
As jbrave mentioned, the Roku does not support directly rendering a web page to the screen. You'll need to write your own functionality to display out the contents.