Based on first-principles density functional theory calculation, we discover a novel form of spin-orbit (SO) splitting in two-dimensional (2D) heterostructures composed of a single Bi(111) bilayer stacking with a 2D semiconducting In₂Se₂ or a 2D ferroelectric α-In₂Se₃ layer. Such SO splitting has a Rashba-like but distinct spin texture in the valence band around the maximum, where the chirality of the spin texture reverses within the upper spin-split branch, in contrast to the conventional Rashba systems where the upper branch and lower branch have opposite chirality solely in the region below the band crossing point. The ferroelectric nature of α-In₂Se₃ further enables the tuning of the spin texture upon the reversal of the electric polarization with the application of an external electric field. Detailed analysis based on a tight-binding model reveals that such SO splitting texture results from the interplay of complex orbital characters and substrate interaction. This finding enriches the diversity of SO splitting systems and is also expected to promise for spintronic applications.