  We study the dihadron fragmentation functions (DiFF) of longitudinally
polarized quarks into pion pairs. The quark-jet framework is used to model the
sequential hadronization of a polarized quark into hadrons, where the
polarization transfer to the remnant quark in each hadron emission step is
calculated using the spin density matrix formalism. Using Monte Carlo (MC)
simulations of the hadronization process, we find a nonvanishing helicity
dependent DiFF, $G_1^\perp$ , which is also related to the longitudinal jet
handedness. A method is developed for extracting the angular moments of this
DiFF, which enter the expressions for the azimuthal asymmetries for an
electron-positron annihilation process into two pairs of hadrons from
back-to-back jets and the dihadron production in semi-inclusive deep inelastic
scattering. Finally, we derive explicit integral expressions for DiFFs where
only two hadrons are emitted by a quark and use them to validate our MC results
for both unpolarized and helicity dependent DiFFs.
