If you know the possible type of the exception (WebException for example, which can be determined during debugging), then try something like this:
Try
'...
Catch exc As Exception
Dim web_exc As WebException = TryCast(exc.InnerException, WebException)
If web_exc IsNot Nothing Then
Dim response As HttpWebResponse = TryCast(web_exc.Response, HttpWebResponse)
If response IsNot Nothing Then
Dim status = response.StatusCode
'...
End If
End If
End Try