Just recently, I read a book of Charles Dickens' complete ghost stories. I had thought that it would be a good book to read right before Halloween, but actually more of the stories had to do with Christmas (including - of course - "A Christmas Carol"). One of them in particular - "The Goblins who Stole a Sexton" - had a lot of references to the Biblical Christmas story; however, it's more of an inversion of those references.
In Dickens' story, the sexton is named Gabriel Grub, and, while he is digging a grave, he encounters some goblins who berate him for doing such dreary work on Christmas. They also are critical of his hitting a kid singing a Christmas song. They say that he "struck the boy in the envious malice of his heart, because the boy could be merry, and he [Gabriel Grub] could not." Then, the goblin king "laid his hand upon his [Grub's] collar, and sank with him through the earth." The goblins show Grub various scenes - and kick him repeatedly - until "he came to the conclusion that it was a very decent and respectable sort of world after all."
There aren't really any large-scale Biblical references, but there are smaller, inverted ones. Dickens' Gabriel Grub is sunk into the earth, which is sort of an inversion of Luke 1, where the angel Gabriel comes to Earth to tell Mary of the eventual birth of Jesus. Similarly, where Dickens' Gabriel deals with death and is pessimistic, the Biblical Gabriel deals with life and is enthusiastic.
I don't think Dickens really meant anything in including these inverted references; I think he just wanted to have some sort of deeper relation between his story and Christmas, so he buried these allusions in his character.