Multiboson production provides a crucial test of the gauge structure of the Standard Model. In this proceeding we present a method to reach NNLO QCD and NLO EW accuracy matched to parton showers using the MiNNLO$_{\mathrm {PS}}$ framework. We show results for the specific case of $W^{\pm}Z$ production with fully leptonic decays, which plays a fundamental role among multiboson processes because of the clean experimental signature and large cross section. We propose different combination schemes between QCD and EW corrections matched to parton showers and we present a phenomenological analysis for LHC collisions, showing that NNLO QCD corrections are dominant in the bulk of the cross section while EW effects become non-negligible in the tails of kinematic distributions. We also present a comparison with recent ATLAS data, finding very good agreement with our theoretical predictions.