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We report a Dalitz-plot analysis of the charmless hadronic decays of
neutral B mesons to K^+/- pi^-/+pi^0. With a sample of
(231.8+/-2.6) 10^6 Upsilon(4S) --> B Bbar decays collected by the BABAR detector
at the PEP-II asymmetric-energy B~Factory at SLAC, we measure the
magnitudes and phases of the intermediate resonant and nonresonant
amplitudes for B^0 and B^0bar decays and determine the corresponding
CP-averaged branching fractions and charge asymmetries. The inclusive branching fraction and CP-violating charge asymmetry are measured to be
BF(B^0 --> K^+pi^-pi^0)=(35.7_{-1.5}^{+2.6} +/-2.2) 10^(-6), and A_CP=-0.030^{+0.045}_{-0.051} +/-0.055
where the first errors are statistical and the second systematic. We observe the decay B^0 --> K^{*0}(892)pi^0
with the branching fraction BF(B^0 --> K^{*0}(892) pi^0)=(3.6_{-0.8}^{+0.7}+/-0.4) 10^(-6)
This measurement differs from zero by 5.6 standard deviations (including the systematic uncertainties).
The selected sample also contains B^0 --> D^0bar pi^0 decays where D^0bar --> K^+pi^-, and we measure
BF(B^0 --> D^0bar pi^0)=(2.93 +/-0.17 +/-0.18) 10^(-4).
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