The ab initio mixed-basis pseudopotential method based on the density-functional theory is applied to study the cohesion, ferromagnetism and electronic structure of iron and iron monohydride with cubic crystal structures. Spin-unpolarized and spin-polarized calculations are used to assess the transferability of norm-conserving ionic pseudopotentials for iron, and the level of accuracy obtainable for structural equations of state with reasonable effort. The influence of generalized gradient corrections on the cohesive properties is investigated. The results are compared directly to corresponding all-electron results obtained by using both FLAPW and LMTO-ASA methods.