It is well known that, combining gauge theory with Freedman's theory, one can find many non-smoothable 4-manifolds. In this talk, I will explain a family version of this story. That is, combining Seiberg-Witten theory for families of 4-manifolds with Freedman's theory, we shall construct plenty of "non-smoothable topological bundles of smooth 4-manifolds". This allows us to show that, for many 4-manifolds, the inclusions from the diffeomorphism groups into the homeomorphism groups are not homotopy equivalences. This talk is based on joint work with Tsuyoshi Kato and Nobuhiro Nakamura, and with David Baraglia.