We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional symmetry protected phases with non-trivial edge properties. We use this exact `decorated-string-net' framework to construct some interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions, on any bipartite graph. Another example is a 3d paramagnet which has anomalous surface topological order.