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)pi(+)pi(-) (n = 1, 2) cross sections from thresholds up to 11.02 GeV. We find clear gamma(10860) and gamma(11020) peaks with little or no continuum contribution. We study the resonant substructure of the gamma(11020) -> h(b)(nP)pi(+)pi(_) 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.