Pain is a protective physiological system essential for survival. However, it can malfunction and create a debilitating disease known as chronic pain (CP). CP is primarily treated with drugs that can have negative side effects (e.g., opioid addiction), and lose efficacy after long-term use. Electrical stimulation of the spinal cord or peripheral nerves is an alternative therapy that has great potential to reduce the need for drugs and has fewer negative side effects; but has been associated with suboptimal efficacy because its modulation mechanisms are unknown. Critical to advancing CP treatment is a deeper understanding of how pain is processed in the superficial and deep layers of the dorsal horn (DH), which is the first central relay station for pain processing in the spinal cord. Mechanistic models of the DH have been developed to investigate modulation mechanisms but are non-linear and high-dimensional and thus difficult to analyze. In this paper, we construct a tractable computational model of the DH in rats from LFP recordings of the superficial layer network and spiking activity of WDR neurons in the deep layer. By combining a deterministic linear time-invariant model with a stochastic point process model, we can accurately predict responses of the DH circuit to electrical stimulation of the peripheral nerve. The model is computationally efficient, low-dimensional, and able to capture the stochastic nature of neuronal dynamics in the DH; and is a first step in developing new therapies for CP.