Using data collected with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider, we measure the energy dependence of the e^{+}e^{-}→h_{b}(nP)π^{+}π^{-} (n=1, 2) cross sections from thresholds up to 11.02 GeV. We find clear ϒ(10860) and ϒ(11020) peaks with little or no continuum contribution. We study the resonant substructure of the ϒ(11020)→h_{b}(nP)π^{+}π^{-} transitions and find evidence that they proceed entirely via the intermediate isovector states Z_{b}(10610) and Z_{b}(10650). The relative fraction of these states is loosely constrained by the current data: The hypothesis that only Z_{b}(10610) is produced is excluded at the level of 3.3 standard deviations, while the hypothesis that only Z_{b}(10650) is produced is not excluded at a significant level.