In order to better understand hydride formation in zirconium alloys, heterophase interfaces between α-Zr and γ-ZrH are investigated by means of ab initio atomic-scale simulations of multilayers coupled with continuous elasticity. Our approach allows us to separate out the elastic contribution, leading to basal and prismatic interface energies around 200 and 750 respectively, i.e. values noticeably higher than previously found for coherent particles such as ζ-Zr2H. By considering interfacial changes of H contents, the possibility of competing elasticity and chemistry effects for interface stability is analyzed. The effects of the strong anisotropy evident in interface energies on the important practical issue of preferential habit planes are discussed, allowing us to propose a plausible explanation for the experimental results.