We present a comprehensive study of band offsets and band bending at heterovalent semiconductor heterointerfaces. A perfectly abrupt heterovalent interface is usually thermodynamically unstable, and atomic intermixing of materials with different numbers of valence electrons causes large variations in band offsets and local doping density, depending on the spatial arrangement of atoms at the interface. The studied prototypical II-VI/III-V semiconductor interfaces are $n$-doped ZnSe/GaAs (001) heterostructures with varied composition profiles close to the interface, which were realized by molecular-beam epitaxy with different amounts of Zn or Se predeposited on $n$-GaAs prior to $n$-ZnSe layer growth. The samples are characterized by temperature-dependent electrical transport across the interface, electrochemical capacitance-voltage profiling, Raman spectroscopy, and high-resolution x-ray diffraction. We find that the potential barrier in the conduction band at a Zn-rich $n$-ZnSe/$n$-GaAs interface is as high as 550 meV and it gradually decreases with Se predeposition down to about 70 meV. A large depletion region at the heterointerface, about 50 nm wide, is assigned to significant intermixing of acceptor-type atoms, resulting in an effective electron deficit of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }{\text{cm}}^{\ensuremath{-}2}$. The depletion width and the acceptor density around the interface are nearly independent from the growth start procedure. Se predeposition, however, partially shifts the depletion region at the heterointerface from GaAs into ZnSe, compared to Zn predeposition. The results are discussed on the basis of a band-bending model accounting for variable band offsets, interface state density and atomic interdiffusion profiles depending on growth start.