The Drell-Yan production of charged lepton pairs is one of the key processes measured at hadron colliders. The QCD corrections to the cross-section are known to order $\alpha_s^2$ and electroweak corrections are known to order $\alpha$. The next important step for a better theoretical understanding is the complete calculation of the mixed QCD-EW corrections of order $\alpha_s \alpha$. In this talk, I report on the first calculation of the virtual two-loop corrections of order $\alpha_s\alpha$ to the cross-section. The calculation is carried out analytically using tensor reduction, IBP relations and the method of differential equations. We validate a previous calculation of the subset of mixed QCD-QED corrections and show how the jet and soft functions of that reference can be used to subtract the infrared divergencies of the complete mixed QCD-electroweak virtual corrections.