Humbert taught at the Sorbonne, the École Normale de Musique de Paris, and the Conservatoire de Musique de Paris.
Humbert wrote numerous classical pieces, including:
- Two symphonies
- Three piano concertos
- Two violin concertos
- A cello concerto
- A flute concerto
- A clarinet concerto
- A bassoon concerto
- A trumpet concerto
- A trombone concerto
- A tuba concerto
- A harp concerto
- A guitar concerto
- A mandolin concerto
- A balalaika concerto
- A domra concerto
- A bayan concerto
- A chamber opera
- Numerous chamber pieces
- Lieder
In addition, Humbert also composed music for several ballets, films, and television programs.