  We propose the 14-band $\mathbf k \cdot \mathbf p$ model to calculate
spin-orbit splittings of the valence subbands in semiconductor quantum wells.
The reduced symmetry of quantum well interfaces is incorporated by means of
additional terms in the boundary conditions which mix the $\Gamma_{15}$
conduction and valence Bloch functions at the interfaces. It is demonstrated
that the interface-induced effect makes the dominating contribution to the
heavy-hole spin splitting. A simple analytical expression for the interface
contribution is derived. In contrast to the 4$\times$4 effective Hamiltonian
model, where the problem of treating the $V_z k_z^3$ term seems to be
unsolvable, the 14-band model naturally avoids and overcomes this problem. Our
results are in agreement with the recent atomistic calculations [J.-W. Luo et
al., Phys. Rev. Lett. {\bf 104}, 066405 (2010)].
