  We investigate heavy-hole--light-hole mixing in quasi-two-dimensional
semiconducting structures. We propose and analyze several measures that
characterize the mixing quantitatively in Ge, Si, and GaAs. We find that a
mixing that is `weak' when considering the light-hole content can be `strong'
when considering the induced spin-orbit interactions (SOIs). We identify two
different types of hole-Hamiltonian terms concerning mixing. The first type
changes the direction of the pure spinors, without admixing light-hole
components. It is efficient for Rabi driving the heavy-hole spin. The second
type induces mixing and changes the eigenvalues of the $g$ tensor. We restrict
ourselves to the zone center, what leads to a simple description, analytical
results, and physical insights. We show how the model can be used to
investigate heavy-hole spin qubit $g$ tensor, dephasing, relaxation, and Rabi
frequencies.
