  Iron-based superconductors can be categorized as two types of parent
compounds by considering the nature of their temperature-induced phase
transitions; namely, first order transitions for 122- and 11-type compounds and
second-order transitions for 1111-type compounds. This work examines the
structural and magnetic transitions (ST and MT) of CaFeAsH by specific heat,
X-ray diffraction, neutron diffraction, and electrical resistivity
measurements. Heat capacity measurements revealed a second-order phase
transition accompanies an apparent single peak at 96 K. However, a clear ST
from the tetragonal to orthorhombic phase and a MT from the paramagnetic to
antiferromagnetic phase were detected. The structural (Ts) and N\'eel
temperatures (TN) were respectively determined to be 95(2) and 96 K by X-ray
and neutron diffraction and resistivity measurements. This small temperature
difference, Ts - TN, was attributed to strong magnetic coupling in the
inter-layer direction owing to CaFeAsH having the shortest lattice constant c
among parent 1111-type iron arsenides. Considering that a first-order
transition takes place in 11- and 122-type compounds with a short inter-layer
distance, we conclude that the nature of the ST and MT in CaFeAsH is
intermediate in character, between the second-order transition for 1111-type
compounds and the first-order transition for other 11- and 122-type compounds.
