Not closet geologist, but close enough. I actually get paid.
Mica's are typically much softer and lighter, and are "sheet-like" so they don't survive the beach energy that well.
It's a mineral called ilmenite. The reason you see it in layers is because it is heavier then quartz and as hard. It makes up about 2-3% of the sand on the beach. So, when storms come in and "re-work" all the sand on the beach, the lighter sand is pulled offshore (quartz) and typically a thin layer or crust forms on top of the remaining sand. Then as the quartz makes its way back on shore, it covers up that crust forming the layers. You can actually get an idea of storm history and smaller erosional and accretional events based on those layers.
As for peat, it does underly our beaches and is also dark/black. The reason is just what was posted earlier, there use to be a marsh where our beaches are now. The difference is that the peat is oily to the touch and typically requires mineral spirits to remove. In many areas the peat is only a few feet (less than 3) under the white sandy beaches. So, if you are seeing it in layers and it feels like sand, it is likely ilmenite. If it is in clumps and is oily, it is likely peat.
If you want to see the peat, go look in the dunes in Seacrest in front of Tranquility by the Sea, or the beach in the Seacrest area after a hurricane or tropical storm.