Heat capacities of the organic-inorganic composite magnets (AMe)3TOT•+•FeIIIBr4-(A = S, Se) were measured by relaxation method under magnetic fields. Heat capacity peaks were observed at 4.93 K and 6.51 K for S and Se compounds, respectively. These peaks are due to antiferromagnetic phase transitions because the peak temperatures decreased slightly as the magnetic fields increased. The experimental magnetic entropies amounted to 19.6 J K-1mol-1 for the S compound and 19.0 J K-1mol-1 for the Se compound, which agree well with the expected value Rln(2x6) = 20.7 J K-1mol-1 due to the ordering of S = 1/2 and S = 5/2 spins corresponding to (AMe)3TOT•+ and FeIIIBr4-, respectively. The zero-field magnetic heat capacities above the magnetic phase transition temperatures were expressed well by the theoretical heat capacity curves for the high-temperature expansions of S = 1 one-dimensional antiferromagnetic Heisenberg models with the intrachain magnetic interactions J/kB = -3.4 K for the S compound and J/kB = -3.0 K for the Se compound. From the mean-field approximation by use of the derived intrachain magnetic interactions and the magnetic phase transition temperatures, the interchain magnetic interactions were estimated to be |zJ′/kB| &asymp1.8 K for the S compound and |zJ′/kB| &asymp 3.5 K for the Se compound.