We present ab initio studies of band offsets, formation energy, and stability of (100) heterojunctions between (Zn,Be)(Se,Te) zinc-blende compounds, and in particular of the lattice-matched BeTe/ZnSe interface. Equal band offsets are found at Be/Se and Zn/Te abrupt interfaces, as well as at mixed interfaces, in agreement with the established understanding of band offsets at isovalent heterojunctions. Thermodynamical arguments suggest that islands of non-nominal composition may form at the interface, causing offset variations over $\ensuremath{\sim}0.8 \mathrm{eV}$ depending on growth conditions. Our findings reconcile recent experiments on BeTe/ZnSe with the accepted theoretical description.