Topological insulators are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of topological insulators have been well studied, the interface between topological insulators and semiconductors may not only be more technologically relevant, but the interaction with non-topological states may fundamentally alter the physics. Here, we present a general model to show that this type of interaction can lead to vertical twinning of the Dirac cone, whereby the hybridized non-spin-degenerate interfacial states cross twice as they span the bulk bandgap. This hybridization leads to spin–momentum locking of non-topological states with either helical (clockwise or anticlockwise) or even anti-helical (negative winding number) spin orientation depending on the parametrization of the interaction. Model results are corroborated by first-principles calculations of the technologically relevant Bi2Se3 film van der Waals bound to a Se-treated GaAs substrate.