The new WebBrowser control in Silverlight 4 is capable of showing HTML content based on a URI or string within your Silverlight application. There are just 2 gotcha’s:

1. At this moment the WebBrowser control will only work if the application runs in Out of the Browser mode. Like you suspect by the name, in this mode the application doesn’t run in the browser anymore but will run locally like a normal desktop app. You have to enable OOTB mode explicitly in Visual Studio. You’ll find this option in the Silverlight project properties pages.

2.  During the install the client needs to give the Silverlight application permissions to travel over the web. So there is an extra option you have to set to get this control working. Check the Require elevated trust when running outside the browser option in the Out-of-Browser Settings dialog.