The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims to discover subdwarf-B stars with massive compact companions such as overmassive white dwarfs (M > 1.0 M⊙), neutron stars or black holes. From the 127 subdwarfs with substantial radial-velocity variations discovered in the initial survey, a number of interesting objects have been selected for extensive follow-up. After an initial photometry run with BUSCA revealed that FBS 0117+396 is photometrically variable both on long and short timescales, we chose it as an auxiliary target during a 6-night multi-color photometry run with Ultracam. Spectroscopy was obtained at a number of observatories in order to determine the binary period and obtain a radial-velocity amplitude. After establishing an orbital period of P = 0.252 d, and removing the signal associated with the irradiated hemisphere of the M-dwarf companion, we were able to detect ten pulsation periods in the Fourier spectrum of the light curve. Two pulsation modes are found to have short periods of 337 and 379 s, and at least eight modes are found with periods between 45 min and 2.5 h. This establishes that FBS 0117+396 is an sdB+dM reflection binary, in which the primary is a hybrid pulsator, and the first one found with this particular mélange of flavours.