Thanks Sozobe. My daughter is 7 and very bookish.
By "treat it as religion", I am comparing the Bible story books I have seen with the Usborne Mythology books (that we like very much). In the Mythology books the focus is on the storytelling. The stories are treated as literature with attention paid to atmosphere and setting and the characters. The fierceness of Fenris, or the oddness of the all-powerful fates or the cowardly treachery of Eurytheus are all wonderful parts of the stories that are illustrated with great love and artistry in these stories.
In the Bible story books I have seen, the focus is on religious facts and devotion. The art of storytelling is not a priority. I feel that so much is lost in the telling of these stories because of the religious focus. I realize that the role of the Christian religion in our culture might make this difficult.
We may end up with "Classic Bible Stories". The excerpts I read didn't excite me.
The "World Tales" book you recommend looks wonderful. Fortunately Amazon has it in stock!