Summary: An integrable vertex model associated to the Lie superalgebra \(sl(2\mid 1)\) is constructed for the description of the spin quantum Hall critical phase. The model involves \(R\)-matrix solutions of the Yang-Baxter equation with respect to both the vector representation of \(sl(2 \mid 1)\) and its dual and an inhomogeneity in the spectral parameters. On the torus the model can be mapped onto a Chalker-Coddington-type network model.