Three major types of GABAergic interneurons, the parvalbumin- (PV), somatostatin- (SOM) and vasoactive intestinal peptide-expressing (VIP) cells, play critical but distinct roles in the cortical microcircuitry. Their inhibitory functions are shaped by their specific electrophysiology and connectivity. To study how this diversity contributes to the dynamics and signal processing in the cerebral cortex, we developed a multi-layer model incorporating biologically realistic parameters of these interneurons from rodent somatosensory cortex. With in vivo data as criteria, the model shows plausible resting-state activity and responses to sensory stimulation. With a protocol of cell-type-specific stimulation, network responses when activating different neuron types are examined. The model reproduces the experimentally observed inhibitory effects of PV and SOM cells and disinhibitory effect of VIP cells on excitatory cells. In addition, responses of VIP cells to cell-type-specific stimulation provide predictions for future experiments. We further create a version of the model incorporating cell-type-specific short-term synaptic plasticity (STP). While the ongoing activity with and without STP is similar, STP modulates the responses of SOM and VIP cells to cell-type-specific stimulation, presumably by changing the dominant inhibitory pathways. Our model can serve to explore the computational roles of inhibitory interneurons and short-term synaptic plasticity in sensory functions.