Accessing a secure site (https) through a Proxy Server requiring authentication

Question

I am adding code to use a proxy server to access the Internet. The code works fine when requesting a file from a normal (HTTP) location, but does not work when accessing a secure location (HTTPS).

This is the code that works just fine:

URL = "http://UnSecureSite.net/file.xml"
Dim wr As HttpWebRequest = CType(WebRequest.Create(URL), HttpWebRequest)
Dim proxy As System.Net.IWebProxy
proxy = WebRequest.GetSystemWebProxy
wr.Proxy.Credentials = System.Net.CredentialCache.DefaultCredentials
Dim ws As HttpWebResponse = CType(wr.GetResponse(), HttpWebResponse)

// (more work here)

As soon as I change the URL to go to HTTPS, I get a 407 returned to me.

Almost like the proxy settings have been cleared.

URL = "https://SecureSite.net/file.xml"
Dim wr As HttpWebRequest = CType(WebRequest.Create(URL), HttpWebRequest)
Dim proxy As System.Net.IWebProxy
proxy = WebRequest.GetSystemWebProxy
wr.Proxy.Credentials = System.Net.CredentialCache.DefaultCredentials
Dim myCache As New CredentialCache()
myCache.Add(New Uri("https://SecureSite.net"), "Basic", New NetworkCredential(UserName, Password))
wr.Credentials = myCache
Dim ws As HttpWebResponse = CType(wr.GetResponse(), HttpWebResponse)

// (more work here)

Does anyone have a solution?   Any help would be appreciated.