  We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated
3-manifolds with surface, line and point defects. Surface defects are oriented
embedded 2d PL submanifolds and are labeled with bimodule categories over
spherical fusion categories with bimodule traces. Line and point defects form
directed graphs on these surfaces and labeled with bimodule functors and
bimodule natural transformations. The state sum is based on generalised 6j
symbols that encode the coherence isomorphisms of the defect data. We prove the
triangulation independence of the state sum and show that it can be computed in
terms of polygon diagrams that satisfy the cutting and gluing identities for
polygon presentations of oriented surfaces. By computing state sums with defect
surfaces, we show that they detect the genus of a defect surface and are
sensitive to its embedding. We show that defect lines on defect surfaces with
trivial defect data define ribbon invariants for the centre of the underlying
spherical fusion category.
