We identify the Brillouin scattering spectrum in both the core and the cladding of an all-solid photonic bandgap fiber for the first time to our knowledge. A multipeak Brillouin spectrum with several frequency shifts and particular linewidths is investigated and related to the structural properties accordingly. Because of the different frequency dependences on the surroundings in the core and the cladding, the proposed structure exhibits potential for use as simultaneous temperature and strain sensors.