We demonstrate the feasibility of fabricating heterojunctions of semiconductors with high mismatches in lattice constant and coefficient of thermal expansion by employing nanomembrane bonding. We investigate the structure of and electrical transport across the interface of a Si/Ge bilayer formed by direct, low-temperature hydrophobic bonding of a 200 nm thick monocrystalline Si(001) membrane to a bulk Ge(001) wafer. The membrane bond has an extremely high quality, with an interfacial region of ∼1 nm. No fracture or delamination is observed for temperature changes greater than 350 °C, despite the approximately 2:1 ratio of thermal-expansion coefficients. Both the Si and the Ge maintain a high degree of crystallinity. The junction is highly conductive. The nonlinear transport behavior is fit with a tunneling model, and the bonding behavior is explained with nanomembrane mechanics.