In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric-field-dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this paper, we present angle-resolved photoemission spectroscopy data which show with high resolution the electronic band structure of trilayer graphene obtained on α-SiC(0001) and β-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic hopping parameters for Bernal and rhombohedral stacked trilayers. Low-energy electron microscopy measurements demonstrate that the trilayer domains extend over areas of tens of square micrometers, suggesting the feasibility of exploiting this material in electronic and photonic devices. Furthermore, our results suggest that, on SiC substrates, the occurrence of a rhombohedral stacked trilayer is significantly higher than in natural bulk graphite.