[en] Magnetic and iron-57 Mossbauer spectral measurements between 4.2 and 640 K have been carried out on TbFe11Ti and TbFe11TiH. The insertion of hydrogen into TbFe11Ti form TbFe11TiH increases its ordering temperature, magnetization, magnetic hyperfine fields, and isomer shifts as a result of lattice expansion. Further, the insertion of hydrogen reinforces the basal magnetic anisotropy of the terbium sublattice and, as is shown by ac susceptibility measurements and thermomagnetic analysis, the spin reorientation observed in TbFe11Ti at 338 K disappears in TbFe11TiH. The Mossbauer spectra have been analysed with a model that considers both the easy magnetization direction and the distribution of titanium atoms in the near-neighbour environment of the three crystallographically distinct iron sites. The assignment and the temperature dependencies of the hyperfine fields and isomer shifts are in complete agreement with a Wigner-Seitz cell analysis of the three iron sites in RFe11Ti and RFe11TiH, where R is a rare-earth element. A complete analysis of the quadrupole interactions in both magnetic phases and in the paramagnetic phase of TbFe11Ti supports the Mossbauer spectral analysis, and indicates that in the basal magnetic phase the iron magnetic moments are oriented along the equivalent  and  directions of the unit cell.