Tree-level Interference in VBF production of $Vh$

We study the production of the Higgs in a association with a vector ($V=W,Z$) via the VBF process, VBF-VH. In the Standard Model (SM), this process exhibits tree-level destructive interference between between $W$ and $Z$ mediated processes and is thus very sensitive to deviations in Higgs couplings to vector bosons. We study this process at both the HL-LHC as well as future high energy lepton colliders. We show in particular that the scenario where Higgs couplings have the same magnitude but opposite relative sign as in the SM, a scenario that is very difficult to distinguish without interference, can be probed with this process at either collider.