Single crystals of CuInS2 were grown by a chemical vapor transport method using ICl3 as a transport agent. The electronic structure of CuInS2 was experimentally characterized by temperature-dependent thermoreflectance (TR) measurements in a wide energy range of 1.25-6 eV between 20 and 320 K. A pair of excitonic doublets of E-1(d)(ex1) and E-1(d)(ex2) near 3.4 eV were observed in the low temperature TR spectrum at 20 K. The temperature- energy shift of the E-1(d)(ex1) and E-1(d)(ex2) features identified the origin of the excitonic doublets. The E-1 excitons were confirmed to be interband transitions from the nonbonding Cu 3d state in the valence band (E-V) to the S 3p antibonding state at the conduction band (E-C) bottom. There were also a lot of derivative-like spectral features observed near the bandedge as well as high lying interband transitions of CuInS2. The origins of the critical-point transitions of CuInS2 were evaluated. X-ray photoelectron spectroscopic (XPS) measurements were implemented to identify the band blocks below the top of the valence band. Based on the experimental analyses of TR and XPS, together with previous band-structure calculations of CuInS2, an experimental band structure that describes a fundamental band-edge structure of CuInS2 was then constructed.