make the ISR a friend function of the class so it can access protected data members. Class member functions cannot be ISR handlers, you will need some reference to an instance of the class that is accessible by the ISR, maybe have a static pointer in the class signifying which instance is currently being used.
If you only intend to have one instance running, you could even make the class a wrapper of static functionality ( comparable to a namespace ), no need to initialise an object then.