I've never been to a church that did that (been through several denominations). Linking all my church time together (and that's a lot), if I hadn't read the Bible through and through, over and over, I would not have got the whole thing in a church.
How is it possible, if you have been to a Roman Catholic church, or a Baptist, Methodist, Episcopal, Lutheran, Presbyterian or any other Protestant church? There is a reading from the Old Testament and from the New Testament at every Sunday service, as well as in any significant rite such as marriage. The old-time hymns are based in the scriptures. After the readings, the reader says, "The Word of the Lord," and the congregation replies, "Thanks be to God."
The churches have a calendar for their readings, which often are similar across denominations. Here is the schedule of readings for the Episcopal church, for instance. Click on the "BCP" or "RCL" links in the Sunday boxes to see the readings. You can find the calendars for other denominations online.