What you're attempting to do is pass credentials via HTTP basic auth, I'm not sure if the username:password syntax is supported in HttpListener, but if it is, you'll need to specify that you accept basic auth first.
HttpListener listener = new HttpListener();
listener.Prefixes.Add(uriPrefix);
listener.AuthenticationSchemes = AuthenticationSchemes.Basic;
listener.Start();
Once you receive a request, you can then extract the username and password with:
HttpListenerBasicIdentity identity = (HttpListenerBasicIdentity)context.User.Identity;
Console.WriteLine(identity.Name);
Console.WriteLine(identity.Password);
Here's a full explanation of all supported authenitcation methods that can be used with HttpListener.