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We present an in-depth study of the spin-orbit (SO) interactions occurring in inversion-asymmetric two-dimensional hole gases at semiconductor heterointerfaces. We focus on common semiconductors such as GaAs, InAs, InSb, Ge, and Si. We develop a semianalytical variational method to quantify SO interactions, accounting for both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA). Under certain circumstances, using the Schrieffer-Wolff (SW) transformation, the dispersion of the ground state heavy hole subbands can be written as where , and are material- and structure-dependent coefficients. We provide a simple method of calculating the parameters , and , yet demonstrate that the simple SW approximation leading to a SIA (Rashba) spin splitting frequently breaks down. We determine the parameter regimes at which this happens for the materials …