In Catholic schools, it was hit or miss, mostly because of the times, and my particular diocese. I remember in 10th grade we read much of the Old Testament, like Ruth, Esther, and Judges. Of course, around Christmas, we read the Gospel accounts. And somewhere, we read the differing Creation stories. Of course, during Lent we read the accounts of the Passion.
I agree that I am not a chapter and verse guy. I also admit I should know a heck of a lot more. Fortunately, I have a pretty good textual concordance, and the Haydock Bible (which has excellent commentary).