This is currently not possible; this is due to the way the web browser control is rendered. This is actually not a real WPF control, but a WPF wrapper around a COM component. This limits the functionality available and causes other problems, such as the inability to float WPF controls on top of it.
I believe that a new WebView control has appeared for Windows 8.1 applications (demo at Build 2013). This can provide more flexibility, although I'm not sure if this application is for Windows 8.1 or it will also be available for WPF applications as part of .NET 4.5.1.
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