The response of the CMS barrel calorimeter (electromagnetic plus hadronic) to hadrons, electrons and muons over a wide momentum range from 2 to 350 GeV/c has been measured. To our knowledge, this is the widest range of momenta in which any calorimeter system has been studied. These tests, carried out at the H2 beam-line at CERN, provide a wealth of information, especially at low energies. The analysis of the differences in calorimeter response to charged pions, kaons, protons and antiprotons and a detailed discussion of the underlying phenomena are presented. We also show techniques that apply corrections to the signals from the considerably different electromagnetic (EB) and hadronic (HB) barrel calorimeters in reconstructing the energies of hadrons. Above 5 GeV/c, these corrections improve the energy resolution of the combined system where the stochastic term equals 84.7 +/- 1.6% and the constant term is 7.4 +/- 0.8%. The corrected mean response remains constant within 1.3% rms.