Measurements of the differential branching fraction and angular moments of the decay B0 → K+π−μ+μ− in the K+π− invariant mass range 1330 < m(K+π−) < 1530 MeV/c2 are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 fb−1 collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, q2, between 0.1 and 8.0 GeV2/c4. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the q2 range 1.1-6.0 GeV2/c4.