We perform a thorough theoretical analysis of the band-offset problem at strained Si/Ge interfaces. The difference between the two materials is small enough to warrant a linear-response treatment: Owing to this feature, chemical and elastic effects can be studied independently. Our main finding is that the band offset is a bulk property, depending only upon the macroscopic strain present in the two materials far from the interface, and independent of any interface feature, such as abruptness, interface strain, or buckling. In agreement with previous work, our results also indicate that the strain variations affect only weakly the valence-band offset, when it is measured between the averages of the split manifolds in the two materials. Starting from these reference levels, simple band-structure effects are responsible for a rather large strain-induced tunability of the offset between the topmost valence states.