Your question is a bit confusing: if you're using an instance of the Net.WebClient class, the Net.WebResponse doesn't enter into the equation (apart from the fact that it's indeed an abstract class, and you'd be using a concrete implementation such as HttpWebResponse, as pointed out in another response).
Anyway, when using WebClient, you can achieve what you want by doing something like this:
Dim wc As New Net.WebClient()
Dim LocalFile As String = IO.Path.Combine(Environment.GetEnvironmentVariable("TEMP"), Guid.NewGuid.ToString)
wc.DownloadFile("http://example.com/somefile", LocalFile)
If Not wc.ResponseHeaders("Content-Type") Is Nothing AndAlso wc.ResponseHeaders("Content-Type") <> "text/html" Then
IO.File.Delete(LocalFile)
Else
'//Process the file
End If
Note that you do have to check for the existence of the Content-Type header, as the server is not guaranteed to return it (although most modern HTTP servers will always include it). If no Content-Type header is present, you can fall back to another HTML detection method, for example opening the file, reading the first 1K characters or so into a string, and seeing if that contains the substring <html>
Also note that this is a bit wasteful, as you'll always transfer the full file, prior to deciding whether you want it or not. To work around that, switching to the Net.HttpWebRequest/Response classes might help, but whether the extra code is worth it depends on your application...