One of the things we want to teach our kids at Southside is seeing the Bible as God's One Big Story. We try to focus every lesson at every level on what God is doing in each Bible story.
Charlie Boyd, our directional leader, wrote a children's book called What God has Always Wanted.
Charlie's book gives a great picture of God's story at its basic level. You can easily read it with a child in one setting. This is clearly a story book and not a bible.
The illustration are wonderful too.
I am currently writing the curriculum we will use this summer in the 3rd and 4th grade. I have been using Sally Lloyd-Jones' book The Jesus Storybook Bible: Every Story Whispers His Name.
I really like this book. It does a great job of telling the one big story, God's story. What I am really impressed with, is how Sally brings God's love for His children to the surface of the story.
This is more of a bible and less of a story book.