This isn't really what the SDK was designed for. It doesn't support embedding and more or less by design, is very painful to use any windows GUI elements in it. There are some ways you could get around this, but you'll be fighting StreetDeck all the way.
If you want to browse the web in a generic sense, you should just launch a web browser as an external application. Yes, there is a need to make ie or whatever browser more touchscreen friendly for use while your stopped, but StreetDeck does not address this yet. The current focus is on driver friendly applications. If you want to access some specific content from the web and display it in StreetDeck in a way that is usable while driving, you should download the content as html or xml, parse it, then use the StreetDeck SDK to display it in a touchscreen friendly form. i.e. like a nav enabled movie listing or weather content.