Like Fred stated, the finish probably is shellac. If it comes off with alcohol, it is shellac.
If it is shellac then you are in luck -- The great thing about shellac is that it is very easy for you to refinish the portions with the orange peel. Use superfine steel wool, dip it in denatured alcohol, and rub it across the orange peel. The denatured alcohol will dissolve the shellac and the steel wool will take off the residue. Rub it only enough to remove the orange peel -- if you rub too much the finish will be stripped completely. The residual dissolved shellac in the denatured alcohol will be deposited on the wood and it will look like a new shellac finish, although not as thick and shiny. Remember, rub only enough to remove the orange peel and don't rub too hard.
Formby's makes a furniture refinisher that will dissolve the shellac and redosit a finish on the wood. Try this if the pure denatured alcohol is too strong.