Neutron diffraction was used to determine the deuterium sites in TbNiAlD_1.28 and TbNiAlD_0.8. Both samples were found to crystallize in the orthorhombic Amm2 space group. Our analysis reveals that deuterium in TbNiAlD_1.28 occupies positions at x=0 and x=1/2 only, while TbNiAlD_0.8 shows the formation of two different phases. For TbNiAlD_1.28, additional magnetic reflections are observed below 16 K indicating antiferromagnetic order. On the other hand, at 10 K, only one of the TbNiAlD_0.8 phases was found to be magnetic. In addition, our study of the localized vibrations of hydrogen in TbNiAlH_1.39 and in its non-magnetic analog YNiAlH_1.35 using inelastic neutron scattering supports the existence of two different hydrogen sites in the saturated hydrides.