winform interacting with embeded webbrowser contrl

There are ways using COM objects which I find complicated because on the client side you must use some <object> tags and it is using com behind the scene.

I prefer calling a scripts to speak to the page from C#

private void RunScript(string cmd, params object[] args)
{
   var doc = WebBrowser1.Document;
   if (doc != null) doc.InvokeScript(cmd, args);
}

This unfortunately won't return anything.
To get data back you can either make a call to a local TCP port. If your program already must provide pictures or pages it is ideal.
If you prefer you can use javascript to change the title. (this is also using jQuery in this sample):

$(".button").click(function () {
   document.title = "#click:" + $(this).attr('id');
});

Then it is easy in your program

void webBrowser1_DocumentTitleChanged(object sender, EventArgs e)
{
   if (webBrowser1.DocumentTitle.StartsWith("#click:"))
   {
      ...
   }
}

</object>