We have performed polarization-selective magneto-photoluminescence (PL) experiment in the Faraday geometry at 1.5 K on a series of self-assembled quantum dots (QDs) in the form of single QD layer and double QD layer systems. The intensities of the PL peaks from two QD layers exhibited significant differences for the two circular polarizations when a magnetic field was applied. This has led to a large difference in the degree of spin polarization between the CdSe and CdZnSe QDs in the double layer system, in contrast to the behavior shown by the quantum dots in the single-layer CdSe or CdZnSe QD structures, both of which show nearly identical dependence of the PL polarization on the field. The observed behavior was interpreted in terms of anti-parallel spin interaction between carriers localized in pairs of QDs that are electronically coupled. This effect of spin interaction was enhanced in the magnetic semiconductor double QD structure in which non-magnetic CdZnSe QD layer replaced by magnetic CdZnMnSe QD layer.