Children's religious stories

My daughter is somewhat interested in the Greek myths. She loves hearing about the gods and goddesses and their exploits from some of the more famous stories. It's easy to find books written for kids on the subject too: simpler story structure, illustrations, and the more gruesome bits ever-so-slightly glossed over. I saw three or four suitable books in a single trip to Half Price Books. These books present just the stories as stories and do not try to editorialize or moralize. Also, the stories are pulled out of the source material and re-written to be religiously-neutral, and they do not necessarily follow the rhyme and meter of, say, Homer's texts.

Now I think it's time to start introducing other important religious stories. I'd like to eventually introduce stories from all culturally-important religions, but at first I'd like to begin specifically with stories she'll hear references to in everyday life, ie stories from the Christian Bible. I'd like her to be familiar with, say, the creation myth and the characters in the Bible, and be able to understand the many references and phrases you hear all the time which have their origins in the Bible, so that she's prepared and not utterly confused when someone "in the wild" starts talking about Adam, Moses, Jesus, Solomon, God, or whatever.

There are many Children's Bible story books out there, but all of them I have seen are for geared either for older kids, or for young Christian children. The problem with the latter group is that they are written for children and parents who believe they are true (or at least "symbolically true"). They also sometimes include explicit "moral of the story" and "this applies to you because…" type things which doesn't interest me. Those books may be fine later, but for now I'd like a story book of Bible stories that has the same feel as the books of Greek myths. Namely, "We offer no opinions on if these are literally true or if anyone else believes them. This is merely what happens in the stories."

Maybe it doesn't matter and I'm over-thinking it, but I'd really like the stories to be presented from more of a religiously-neutral standpoint. No, I'm not worried she'll convert to Christianity or something simply by hearing the stories; I merely want to be able to read the stories without having to answer awkward questions from a 4-year-old like "Is that really true?" and "Is that what my friends believe?" When she's old enough to understand religious belief (especially when she's old enough to read it herself), there'll time enough for those stories and questions, then she can have unfettered access to any religious text she wants. But for now, I'd just like for her to be familiar with the stories to prepare her to understand the more abstract parts later. Plus I'd like to avoid any possible nastiness from parents when my daughter informs their kids that "I've thought about it and I think God is probably just a story" (personally, I'd think that'd be awesome, but probably not a good social move).

If you are a religious Christian and are wondering why this is "such big deal": it's not, really. It's just a minor thing, but when it comes to learning about the world, there are good ways and not so good ways. Pretend you wanted to introduce your young child to the stories of Islam, or to learn about what Muslims believe. You probably wouldn't just start reading the Koran (at least I wouldn't), and you probably wouldn't go out and get a book of stories written for Islamic children either: you'd want to get a book that talks about Islam. You'd want a book that tells the stories and doesn't give "moral of the story" things like "Hey kids! Allah wants you to pray 5 times a day!". You'd go for a book that talks about what Muslims believe, or even just the stories themselves, minus the proselytizing.

So far, the one that seems most likely is The Children's Illustrated Bible. In looking at the preview on Amazon, it seems OK, but it doesn't seem to have quite the right "feel" to it. It seems too much of a direct translation of the structure of the Bible stories. I'd like the Bible stories to be extracted from the source and rewritten in the same manner the Greek stories we've been reading.

As I said, I'm not worried it's going to induce a religious belief, I just want to read the stories so she's familiar with the characters and events.

Anyone out there have a more "neutral" book of Bible stories for kids? Am I over-thinking this and should just pick up any old thing?