Hi, Pete. This is pretty tough to tell without seeing it but the brown, thick cardboard sounds like hardboard (also sold under the trade name Masonite). Hardboard has also been sold in a prefinished version with many different types of paint on its surface. You might want to go to a home center and look at the pegboard. This is the same stuff but with holes in it. If you see a piece that has been banged around some on a corner, you will see that it does separate off in layers under the hard, smooth outside.
Pete, my personal feeling is that hardboard is not good for much of anything except pegboard. It has been used in cheap furniture and really does not last over the years. The prepainted hardboard, to my way of thinking, was usually used in cheap installations. Once you are under the smooth original surface, it would be hard to refinish it back to a smooth surface. You might try a little gentle exploring to see what is under the hardboard which might well be glued to drywall or plaster under it. Or I could be on completely the wrong track. Maybe you could do a little investigating and let us know further.