Write a program in C++ that supports both Stack and Queue operations using a doubly linked list. The data structure should include functions:
•For push (to add an element to the top of the stack)
•Pop (to remove and return the top element from the stack)
•Enqueue (to add an element to the back of the queue)
•Dequeue (to remove and return the front element from the queue)
•Additionally, include a function to check if the data structure is empty, as well as a function to display the elements in the structure from front to back."