Spin ordering in TbBaCo2O5.5 and its temperature transformation reproducible for two differently synthesized samples are studied. One of the ceramic samples, in addition to the main phase apx2apx2ap,Pmmm (Z=2), where ap is parameter of perovskite cell, contains about 32% of the phase apxapx2ap,Pmmm (Z=1) with statistical distribution of oxygen over the apical sites. The other sample is a single phase apx2apx2ap,Pmmm (Z=2) with well defined octahedral and pyramidal sublattices. Treatment of neutron diffraction patterns of the double-phase sample itself gives a sophisticated spin structure. Knowing the spin structure of the single-phase sample, one can choose only proper magnetic lines, which give exactly the same results for both samples. The spin structure at T=265K unambiguously indicates the phase 2apx2apx2ap,Pmma (Z=4). At TN≈290K, the spins order with the wave vector k19=0 (phase 1). At T1≈255K, a magnetic transition takes place to the phase 2 with k22=b3 2. The extinction law of magnetic reflections below T2≈170K evidences that the crystal structure changes to 2apx2apx4ap,Pcca (Z=8). The wave vector of the spin structure becomes again k19=0 (phase 3). The basis functions of irreducible representations of the group Gk have been found. Using results of this analysis, the magnetic structure in all phases is determined. The spins are always parallel to the x axis, and the difference is in the values and the mutual orientation of the moments in the ordered nonequivalent pyramidal or octahedral positions. Spontaneous moment M0=0.30(3)μB Co at T=260K is due to ferrimagnetic ordering of the moments MPy1=0.46(9)μB and MPy2=-1.65(9)μB in pyramidal sites (Dzyaloshinskii-Moriya canting is forbidden by symmetry). The moments in the nonequivalent octahedral sites are: MOc1=-0.36(9)μB, MOc2=0.39(9)μB. At T=230K, MPy1=0.28(8)μB, MPy2=1.22(8)μB, MOc1=1.39(8)μB, MOc2=-1.52(8)μB. At T=100K, MPy1=1.76(6)μB, MPy2=-1.76μB, MOc1=3.41(8)μB, MOc2=-1.47(8)μB. The moment values together with the ligand displacements are used to analyze the spin-state/orbital ordering in the low-temperature phase.