The nature of the spin exchange interaction within the half-filled band of one-dimensional stacks of 1-D mixed molecular radical crystals (MMRC) with the general formula: ....PAH....R-.....PAH.....R-.......PAH....R-......PAH....R.(....)(R-., radical; PAH, diamagnetic polycyclic aromatic hydrocarbon) was investigated theoretically. The various contributions to the Heisenberg effective exchange integral, the direct (Coulomb), kinetic, and indirect spin exchange for the MMRCs, are evaluated quantitatively, using band theory, and are compared with those of the corresponding parent molecular radical crystals (MRC, without hydrocarbons). The nature and the magnitude of the exchange interaction in MMRCs are significantly different in comparison with the parent MRCs: the ferromagnetic interaction in MRC changes into antiferromagnetic in MMRCs and vice versa.