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Abstract We construct a large class of conformal interfaces between two-dimensional c = 1 conformal field theories describing compact free bosons and their ℤ 2 $$ {\mathrm{\mathbb{Z}}}_2 $$ orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c = 2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent theory.