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Abstract Turbulent radiative mixing layers (TRMLs) form at the interface of cold, dense gas and hot, diffuse gas in motion with each other. TRMLs are ubiquitous in and around galaxies on a variety of scales, including galactic winds and the circumgalactic medium. They host the intermediate-temperature gases that are efficient in radiative cooling, thus playing a crucial role in controlling the cold gas supply, phase structure, and spectral features of galaxies. In this work, we develop an intuitive analytic 1.5-dimensional model for TRMLs that includes a simple parameterization of the effective turbulent conductivity and viscosity and a piecewise power-law cooling curve. Our analytic model reproduces the mass flux, total cooling, and phase structure of 3D simulations of TRMLs at a fraction of the computational cost. It also reveals essential insights into the physics of TRMLs, particularly the importance of the viscous dissipation of relative kinetic energy in balancing radiative cooling as the shear Mach number approaches unity. This dissipation takes place both in the intermediate-temperature phase, which reduces the enthalpy flux from the hot phase, and in the cold phase, which enhances radiative cooling. Additionally, our model provides a fast and easy way of computing the column density and surface brightness of TRMLs, which can be directly linked to observations.