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We present next-to-leading order QCD and electroweak (EW) theory predictions for $V+2\,$jet production, with $V=Z,W^{\pm}$, considering both the QCD and EW production modes and their interference. We focus on phase-space regions where $V+2\,$jet production is dominated by vector-boson fusion, and where these processes yield the dominant irreducible backgrounds in searches for invisible Higgs boson decays. Predictions at parton level are provided together with detailed prescriptions for their implementation in experimental analyses based on the reweighting of Monte Carlo samples. The key idea is that, exploiting accurate data for $W+2\,$jet production in combination with a theory-driven extrapolation to the $Z+2\,$jet process can lead to a determination of the irreducible background at the few-percent level. Particular attention is devoted to the estimate of the residual theoretical uncertainties due to unknown higher-order QCD and EW effects and their correlation between the different $V+2\,$jet processes, which is key to improve the sensitivity to invisible Higgs decays.