We present the results of THz absorption measurements of monolayer graphene with molecular doping and four-layer graphene. There are several important findings in this study. First, the THz conductivity of the triazine-doped film consists of free carrier absorption at zero frequency and a disorder-induced finite frequency peak around 4.65 THz. As the temperature is lowered, the Drude plasma frequency (30 THz) decreases, whereas the carrier relaxation time (54 fs) does not show much temperature variation. These scenarios show the semiconducting behavior of the triazine-doped film. Second, a comparison of our measured conductance spectra and the theoretical predictions in turn illuminates the importance of the several scattering mechanisms present in these materials. Third, in a magnetic field, the Drude oscillator strength of four-layer graphene is suppressed and transferred to various finite frequency transitions between the Landau levels. The dramatic increase of the low-frequency transmission is a THz counterpart of the positive magnetoresistance effect. The 300 K magnetodielectric contrast is as large as 60% near 1 THz at 10 Tesla. The results are potentially useful for magnetic memory applications away from the dc limit.