(Sr$_{2}$,Ba$_{2}$)Cu$_{3}$O$_{4}$Cl$_{2}$ are antiferromagnetic insulators which are akin to the parent compounds of the cuprate superconductors but with two distinct magnetic ordering temperatures related to two magnetic Cu$_{I}$ and Cu$_{II}$ spin sublattices. Here we present a study of these materials by means of Raman spectroscopy. Following the temperature and polarization dependence of the data we readily identify two distinct features at around 3000 cm$^{-1}$ and 300 cm$^{-1}$ that are related to two-magnon scattering from the two sublattices. The estimated spin-exchange coupling constants for the Cu$_{I}$ and Cu$_{II}$ sublattices are found to be J$_{I}sim$139-143(132-136) meV and J$_{II}sim$14(11) meV for Sr(Ba) compounds. Moreover, we observe modes at around 480 and 445 cm$^{-1}$ for the Sr and Ba containing samples respectively, that disappears at the ordering temperature of the Cu$_{II}$. We argue that this modes may also be of magnetic origin and possibly related to interband transitions between the Cu$_{I}$-Cu$_{II}$ sublattices.
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