I intend to use data binding between a few of my classes. In other words, I am not binding values between a model class and the UI, but to bind variables between different class
I believe I only have access to the the vanilla .Net framework
The reality is that data binding is used in UI. So, if anybody talks about data binding, then he automatically implies "data binding in [UI Framework name]".
You may consider object-to-object mapping instead of data binding.