We report measurements of the specific heat of two samples of carbon-doped MgB2, Mg(B1−xCx)2, x = 0.05 and 0.1, in magnetic fields to μ0H = 9 T and at temperatures from ∼1 K to somewhat above the critical temperature for superconductivity for each sample. The carbon doping reduced the critical temperature from 39 K for MgB2 to 31.4 K and 19.7 K for the x = 0.05 and 0.1 samples, respectively. The results give the electron–phonon coupling and the electron density of states, including the individual contributions of the π and σ bands. These quantities are compared with theoretical calculations. The results also give the energy gaps on the π and σ bands, which are compared with other experimental determinations, and also with theoretical calculations that include predictions of the "merging" of the two gaps as a consequence of the band filling and increased interband scattering associated with doping.