We report a combined experimental/modeling study of optical emission from the A(2)Delta, B-2 Sigma(-) , and C-2 Sigma(+) states of the CH radical in microwave (MW) activated CH4/H-2 gas mixtures operating under a range of conditions relevant to the chemical vapor deposition of diamond. The experiment involves spatially and wavelength resolved imaging of the CH(C -> X), CH(B -> X), and CH(A -> X) emissions at different total pressures, MW powers, C/H ratios in the source gas, and substrate diameters. The results are interpreted by extending an existing 2D (r, z) plasma model to include not just electron impact excitation but also chemiluminescent (CL) bimolecular reactions as sources of the observed CH emissions. Three possible CL reactions (of H atoms with CH2 (a(1)A(1)) and CH2((XB1)-B-3) radicals and of C(D-1) atoms with H-2) are identified as plausible sources of electronically excited CH radicals (particularly of the lowest energy CH(A) state radicals). Each or all of these could contribute to the observed emissions and, collectively, are deduced to be the major source of the CH(A) emissions observed at the high temperatures (T-gas similar to 3000 K) and pressures (75 <= p <= 275 Torr) explored in the present study. We suggest that such CL contributions are likely to be commonplace in such high pressure, high temperature plasma environments and highlight some of the risks associated with using relative emission intensities as an indicator of the electron characteristics in such plasmas.