Due to the relevant contribution of radiative transfer in the global energy balance of many industrial combustion systems, a deep understanding and accurate modelling of gas and soot radiative transfer is necessary. This topic is addressed here numerically in a canonical turbulent sooting configuration, i.e. an ethylene-air jet diffusion flame. The study is based on a coupled Monte Carlo-Large Eddy Simulation. In order to introduce as much physical details as possible, a recently-developed sectional model is used for soot particles description and the radiative transfer equation is solved using a Monte-Carlo method. A cK model describes gas radiative properties and the Rayleigh's theory is considered for soot particles properties. Numerical results are compared to experimental data on radiative intensity measured along the flame height to validate the proposed methodology. Then, the different radiative contributions i.e. emission-absorption, gas-soot, are analyzed to study the nature of the radiative heat transfer in the investigated flame. Finally, turbulence-radiation interactions are quantified for the total mean emitted, absorbed and radiative powers. Closure of these effects on the mean emitted power is proposed and discussed. Opposite effects of turbulence-radiation interactions are observed for the gaseous and the soot contributions: the increase in mean emitted power for the gaseous phase is due to temperature fluctuations whereas a decrease of the solid phase contribution appears from a negative temperature-soot volume fraction correlation.