Semiconductor Bloch equations, in their extension including the spin degree of freedom of the carriers, are capable to describe spin dynamics on a microscopic level. In the presence of free holes, electron spins can flip simultaneously with hole spins due to electron-hole exchange interaction. This mechanism named after Bir, Aronov, and Pikus is described here by using the extended semiconductor Bloch equations [Phys. Status Solidi B 234, 385 (2002)] and considering carrier-carrier interaction beyond the Hartree-Fock truncation. As a result we derive microscopic expressions for spin-relaxation and spin-dephasing rates.