I have created Silverlight Login Page. I use PasswordBox in that page and use this solution to do MVVM in my application. BTW after I read this answer I realize that current solution is not secure.
I want to know how can I improve security in my solution even though it will break MVVM.
You should send the password over HTTPS. The Session ID should also be transmitted over HTTPS at all times or you would be violating OWASP A9 – Insufficient Transport Layer Protection.