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 Neel 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.