You can always write a control that wraps the Password and adds a dependency property for the Password property.
I would just use code behind, but if you must you can do something like:
public class BindablePasswordBox : Decorator
{
    public static readonly DependencyProperty PasswordProperty =
        DependencyProperty.Register("Password", typeof(string), typeof(BindablePasswordBox));
    public string Password
    {
        get { return (string)GetValue(PasswordProperty); }
        set { SetValue(PasswordProperty, value); }
    }
    public BindablePasswordBox()
    {
        Child = new PasswordBox();
        ((PasswordBox)Child).PasswordChanged += BindablePasswordBox_PasswordChanged;
    }
    void BindablePasswordBox_PasswordChanged(object sender, RoutedEventArgs e)
    {
        Password = ((PasswordBox)Child).Password;
    }
}