The mammalian sensory cortex is composed of multiple types of inhibitory and excitatory neurons, which form sophisticated microcircuits for processing and transmitting sensory information. Despite rapid progress in understanding the function of distinct neuronal populations, the parameters of connectivity that are required for the function of these microcircuits remain unknown. Recent studies found that two most common inhibitory interneurons, parvalbumin- (PV) and somatostatin-(SST) positive interneurons control sound-evoked responses, temporal adaptation and network dynamics in the auditory cortex (AC). These studies can inform our understanding of parameters for the connectivity of excitatory-inhibitory cortical circuits. Specifically, we asked whether a common microcircuit can account for the disparate effects found in studies by different groups. By starting with a cortical rate model, we find that a simple current-compensating mechanism accounts for the experimental findings from multiple groups. They key mechanisms are two-fold. First, PVs compensate for reduced SST activity when thalamic inputs are strong with less compensation when thalamic inputs are weak. Second, SSTs are generally disinhibited by reduced PV activity regardless of thalamic input strength. These roles are augmented by plastic synapses. These roles reproduce the differential effects of PVs and SSTs in stimulus-specific adaptation, forward suppression and tuning-curve adaptation, as well as the influence of PVs on feedforward functional connectivity in the circuit. This circuit exhibits a balance of inhibitory and excitatory currents that persists on stimulation. This approach brings together multiple findings from different laboratories and identifies a circuit that can be used in future studies of upstream and downstream sensory processing.