We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin–Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we present an explicit and computable construction of such defects. It specialises to the construction in Carqueville et al. (Geom Topol 23:781–864, 2019. https://doi.org/10.2140/gt.2019.23.781. arXiv:1705.06085) if all 3-strata are labelled by the same topological field theory. We compare the results to the model-independent analysis in Fuchs et al. (Commun Math Phys 321:543–575, 2013. https://doi.org/10.1007/s00220-013-1723-0. arXiv:1203.4568) and find agreement.