We report the experimental and theoretical study of two-body interactions in a Li-6-Cs-133 Fermi-Bose mixture. Using a translatable dipole trap setup, we have successfully trapped the two species in the same trap with temperatures of a few microkelvins. By monitoring atom number loss and interspecies thermalization, we identify five s-wave interspecies Feshbach resonances in the lowest two scattering channels. We construct a coupled channels model using molecular potentials to fit and characterize these resonances. Two of the resonances are as wide as 6 mT (60 G) and thus should be suitable for creating Feshbach molecules and searching for universal few-body scaling. DOI: 10.1103/PhysRevA.87.010702