The resonant substructure of B(s)(0) → D(0)K(-)π(+) decays is studied using a data sample corresponding to an integrated luminosity of 3.0 fb(-1) of pp collision data recorded by the LHCb detector. An excess at m(D(0)K(-))≈ 2.86 GeV/c(2) is found to be an admixture of spin-1 and spin-3 resonances. Therefore, the D(sJ)*(2860)(-) state previously observed in inclusive e(+)e(-) → D(0)K(-)X and pp → D(0)K(-)X processes consists of at least two particles. This is the first observation of a heavy flavored spin-3 resonance, and the first time that any spin-3 particle has been seen to be produced in B decays. The masses and widths of the new states and of the D(s2)*(2573)(-) meson are measured, giving the most precise determinations to date.