We report on heterojunction diodes prepared by exfoliation and direct mechanical transfer of a p-type InSe thin film onto an n-type InAs epilayer. We show that despite the different crystal structures and large lattice mismatch (34%) of the component layers, the junctions exhibit rectification behaviour with rectification ratios of 10[superscript]4 at room temperature and broad-band photoresponse in the near infrared and visible spectral ranges.