A method for making a composite structure with a surfacing film thereon. The surfacing film is co-cured with fiber-reinforced resin composite materials. The surfacing film is formed from a curable resin composition containing an epoxy novolac resin, a tri-functional or tetra-functional epoxy resin, ceramic microspheres, an amine-based curing agent, particulate inorganic fillers; and a toughening component. The surfacing film exhibits high Tg and high cross-linked density after curing, as well as high resistance to paint stripper solutions.