We propose a model that describes the operation characteristics of a two-dimensional electron gas (2DEG) in a monolayer transition-metal dichalcogenide thin-film transistor (TFT) having trapped charges near the channel interface. We calculate the drift mobility of the carriers scattered by charged defects located in the channel or near the channel interfaces. The calculated drift mobility is a function of the 2DEG areal density of interface traps. Finally, we calculate the model transfer (I-D - V-GS) and output (I-D - V-SD) characteristics and verify them by comparing with the experimental results performed with monolayer MoS2 TFTs. We find the modeled results to be excellently consistent with the experiments. This proposed model can be utilized for measuring the interface-trapped charge and trap site densities from the measured transfer curves directly, avoiding more complicated and expensive measurement methods.