We report searches for the processes e+e−→π+π−π0χbJ and e+e−→ϕχbJ (J=1,2) in the vicinity of the Υ(11020) resonance using energy scan data collected by the Belle experiment at the KEKB collider. We observe e+e−→π+π−π0χb1 and find evidence for e+e−→ωχb2 processes for data with center-of-mass energies from 10.96 to 11.05~GeV for the first time. The statistical significance for π+π−π0χb1 and ωχb2 are 6.1σ and 4.0σ, respectively. We investigate energy dependence of the e+e−→π+π−π0χbJ cross section and find that it is consistent with production of Υ(10860) and Υ(11020) resonances without significant non-resonant contribution. Assuming e+e−→π+π−π0χbJ proceeds via Υ(10860) and Υ(11020), the branching fraction (Υ(11020)→π+π−π0χbJ)=(8.6±4.1±6.1+4.5−2.5)×10−3 is measured for the first time, where the first error is statistical, the second is systematic, and the third from the branching fraction of Υ(11020)→e+e−. The signals for e+e−→ϕχbJ are not significant, and the upper limits of the Born cross sections at the 90\% confidence level are 0.6 and 1.0~pb for e+e−→ϕχb1 and ϕχb2, respectively, for center-of-mass energies from 10.96 to 11.05~GeV.