In this paper, we present a progressive compression algorithm for textured surface meshes, which is able to handle polygonal non-manifold meshes as well as discontinuities in the texture mapping. Our method applies iterative batched simplifications, which create high quality levels of detail by preserving both the geometry and the texture mapping. The main features of our algorithm are (1) generic edge collapse and vertex split operators suited for polygonal non-manifold meshes with arbitrary texture seam configurations, and (2) novel geometry-driven prediction schemes and entropy reduction techniques for efficient encoding of connectivity and texture mapping. To our knowledge, our method is the first progressive algorithm to handle polygonal non-manifold models. For geometry and connectivity encoding of triangular manifolds and non-manifolds, our method is competitive with state-of-the-art and even better at low/medium bitrates. Moreover, our method allows progressive encoding of texture coordinates with texture seams; it outperforms state-of-the-art approaches for texture coordinate encoding. We also present a bit-allocation framework which multiplexes mesh and texture refinement data using a perceptually-based image metric, in order to optimize the quality of levels of detail.