The spin dependence of low-energy electron absorption and reflection from ferromagnetic Fe(110) is investigated using the normalized difference between the absorption (or reflection) of electrons polarized parallel and antiparallel to sample magnetization. The resulting absorption and reflection spin asymmetries are found to be reciprocal to each other, with their magnitudes related in a simple manner. Structure in the spin asymmetries is identified with features in the spin-split bulk band structure and is thus found to be related to the spin-polarization fine structure of secondary electrons emitted from the same surface. The general structure of the spin asymmetry as a function of incident energy is dominated by elastic-scattering events, although inelastic scattering is found to play a major role in determining the sign and magnitude of the absorbed and total (energy-integrated) reflected asymmetries. Furthermore, the existence of nonzero elastic-reflection asymmetries indicates the existence of spin-split unoccupied energy bands up to 50 eV above the vacuum level. Inelastic-scattering spin asymmetries show a 2-eV energy-loss feature that is identified as due to the creation of Stoner excitations in the ferromagnet. This feature is determined to be surprisingly insensitive to the incident electron energy (from 0 to 50 eV) and angle (from 0 degrees to 65 degrees from the normal) in contrast to predictions of a recent theory of spin-polarized electron scattering in ferromagnets.