Recently, interlayer exchange-coupling constants in solids of compounds $[\mathrm{N}{\mathrm{H}}_{3}{(\mathrm{C}{\mathrm{H}}_{2})}_{n}\mathrm{N}{\mathrm{H}}_{3}]\mathrm{Cu}{\mathrm{Br}}_{4}$, with $n=3 \mathrm{and} 4$, have been measured by Drumheller et al. Following our earlier theoretical analysis of such compounds with Cl instead of Br for $n=2\ensuremath{-}5$, and one ClBr mixed compound for $n=2$, we apply a four-center, six-electron model to calculate these coupling parameters, assuming a double-halide Cu\char22{}Br\char22{}Br\char22{}Cu superexchange unit. Excellent agreement with the experimental values is obtained. Nonlinearity of the superexchange bridge for $n=4$ is found to be essential to obtain the correct value for the coupling parameter. We perform similar calculations on a layered structure with a Co\char22{}double-oxygen\char22{}Co bridge.