After ten years from its discovery, the Higgs boson is still under unprecedented scrutiny. A huge theoretical effort has been invested in modelling Higgs boson production through gluon fusion, reaching $\text{N}^3\text{LO}$ predictions in pure QCD. This incredible theoretical achievement makes the exact computation of sub-leading contributions, such as mixed QCD-Electroweak corrections, necessary. I will present the analytic calculation of the gluon- and quark-initiated two-loop four-point contributions to such class of corrections mediated by light quarks at order $v \alpha^2 \alpha_S^{3/2}$.