Some quantum interference effects are exposed directly in experiments, but others are not and remain just hidden and thus require thorough theoretical analysis to be exposed. In this respect, the second absorption bands of IX (X = Cl, Br) molecules show an interesting behavior in the photofragment anisotropy of the lowest I((2)P3/2)+X((2)P3/2) product channel; it changes from strongly parallel distribution on the shorter wavelength side to strongly perpendicular distribution on the longer wavelength side. Because the responsible perpendicular third Ω = 1 (1(III)) excited state correlating adiabatically to this product channel has only a weak absorption, the parallel component flux yielding the same products must be comparatively weak, even though the responsible parallel excitations to the 0(+)(III) and/or 0(+)(IV) excited states have strong absorptions. In the present theoretical study, the branching ratios and the anisotropy parameters have been obtained using the spin-orbit configuration interaction method combined with the quantum mechanical wavepacket and semiclassical approaches. Significant quantum interference effect between the two dissociative de Broglie waves on the 0(+)(III) and 0(+)(IV) potential curves has been found through the avoided crossing, and the weak parallel flux to the ground-state product channel has been explained by their destructive interference character. This interference effect has weak excitation energy dependence due to rather unique behavior of their almost parallel potential curves from the Franck-Condon to avoided crossing regions.