This work describes the broadband optical response of graphene grown by chemical vapor deposition by combining terahertz time-domain spectroscopy (THz-TDS) at 0.25-1.7 THz (8-60 cm−1) with Fourier Transform Infrared Spectroscopy (FTIR) at 11-210 THz (370-7000 cm−1). It is shown that the measured response is well described by a combination of the Drude model, expressing free-carrier absorption/reflection, and an expression for interband absorption. The THz-TDS and FTIR transmittance curves are fitted consistently using this model. This indicates that these techniques are complementary to each other. Both can thus be employed together or individually to characterize the electronic properties of graphene (e.g., carrier density and mobility). To exemplify this, we demonstrate that this equivalency can be used to study the effect of substrate-dependent doping on the optical response of graphene. Furthermore, the amount of reflection and absorption corresponding to the measured transmittance curve is calculated. The toolbox for the non-invasive broadband characterization of graphene is thus extended by this work.