We report searches for the processes e+e-→π+π-π0χbJ and e+e-→φχbJ (J=1, 2) based on data samples collected by the Belle experiment at the KEKB collider. We report the first observation of the process e+e-→(π+π-π0)non-ωχb1 and first evidence for e+e-→ωχbJ in the vicinity of the ?(11020) resonance, with center-of-mass energies from 10.96 to 11.05 GeV. The significances for (π+π-π0)non-ωχb1 and ωχbJ are greater than 5.3σ and 4.0σ, respectively. We also investigate the energy dependence of the e+e-→π+π-π0χbJ cross section, but we cannot determine whether the contributions are from the ?(10860) and ?(11020) resonances or nonresonant continuum processes. The signals for e+e-→φχbJ are not significant, and the upper limits of the Born cross sections at the 90% confidence level are 0.7 and 1.0 pb for e+e-→φχb1 and φχb2, respectively, for center-of-mass energies from 10.96 to 11.05 GeV.