This work reports the first observation of azimuthal asymmetries around the thrust axis in e+e- annihilation of pairs of back-to-back charged pions in one hemisphere, and π0 and η mesons in the opposite hemisphere. These results are complemented by a new analysis of pairs of back-to-back charged pions. The π0 and η asymmetries rise with the relative momentum z of the detected hadrons as well as with the transverse momentum with respect to the thrust axis. These asymmetries are sensitive to the Collins fragmentation function H1¥ and provide complementary information to previous measurements with charged pions and kaons in the final state. In particular, the η final states will provide additional information on the flavor structure of H1¥. This is the first measurement of the explicit transverse-momentum dependence of the Collins fragmentation function from Belle data. It uses a dataset of 980.4 fb-1 collected by the Belle experiment at or near a center-of-mass energy of 10.58 GeV.