I believe mouth organs are free reed -

The Hornbostel–Sachs classifications lists
412 Interruptive free aerophones
412.1 Idiophonic interruptive aerophones or reeds
    412.13 Free-reed instruments
       412.132 Sets of free reeds.
          including -
             * Accordion
             * Bandoneon
             * Concertina
             * Harmonica
             * Harmonium
             * Melodica
             * Reed organ
             * Sheng

In contrast the serpent is a
423 Trumpet
   423.2 Chromatic trumpets - The pitch of the instrument can be altered mechanically
      423.21 Keyed trumpets
       including
       * Cornett (or Cornetto - just one)
       * Serpent


I would love to hear the big brother contrabass serpent http://www.music.ed.ac.uk/euchmi/ujt/ujt2929.html

Mitch