In the pursuit of understanding the complex mechanisms of the brain, computational neuroscience employs mathematical models to abstract and simulate processes that govern neural systems. By treating the brain as a dynamical system, these models allow for the exploration of neuronal behaviors and interactions under various conditions. Within this context, mechanistic models of recurrently connected excitatory (E) and inhibitory (I) neural populations allow us to gain unique insights into neuronal computations and functions. Rate-based models, simplify neural dynamics by averaging the activity of neurons and time to produce smooth, analytically tractable, continuous representations of neural activity. Among these, Stabilized Supralinear Networks (SSN) are a prominent category of E/I rate-based models known for capturing essential aspects of cortical dynamics, such as nonlinear integration of visual inputs and modulation of response variability. On the other hand, neural circuits models that explicitly consider spiking events give the chance to study interactions of higher complexity and at finer time scales. Here, we develop a theoretical framework based on linear response theory that incorporates the same nonlinearities of the SSN, while also producing spiking activity following self-exciting Poisson statistics. Our spiking model can capture the main properties of the SSN : nonlinear input balancing, modulation of response variability and input normalization mechanisms. To study the effects of spike timing-dependent plasticity in our framework, we analytically characterize their firing rate and second order statistics in the vicinity of the system's stable point, and infer the expected change in synaptic weights due to plasticity. This analysis sheds light on how variations in input or connectivity structure can affect plasticity, shaping the network’s emergent dynamics.