We investigate the bonding mechanism in ozone (O3) and its sulfur-substituted analogues, SO2, OS2, and S3. By analyzing their ground-state multireference configuration interaction wave functions, we demonstrate that the bonding in these systems can be represented as a mixture of a closed-shell structure with one and a half bonds between the central and terminal atoms and an open-shell structure with a single bond and two lone electrons on each terminal atom (biradical). The biradical character (β) further emerges as a simple measure of the relative contribution of those two classical Lewis structures emanating from the interpretation of the respective wave functions. Our analysis yields a biradical character of 3.5% for OSO, 4.4% for SSO, 11% for S3, 18% for O3, 26% for SOO, and 35% for SOS. The size/electronegativity of the end atoms relative to the central one is the prevalent factor for determining the magnitude of β: smaller and more electronegative central atoms better accommodate a pair of electrons facilitating the localization of the remaining two lone π-electrons on each of the end atoms, therefore increasing the weight of the second picture in the mixed bonding scenario (larger β). The proposed mixture of these two bonding scenarios allows for the definition of the bond order of the covalent bonds being (3-β)/2, and this accounts for the different O-O, S-S, or S-O bond lengths in the triatomic series. The biradical character was furthermore found to be a useful concept for explaining several structural and energetic trends in the series: larger values of β mark a smaller singlet-triplet splitting, closer bond lengths in the ground (1)A' and the first excited (3)A' states, and larger bond dissociation and atomization energies in the ground state. The latter explains the relative energy difference between the OSS/SOS and OOS/OSO isomers due to their different β values.