Today, searching for materials hosting quantum anomalous Hall effect (QAHE) at high temperature and with long conductivity plateau is an important issue for next generation spintronic applications at nanoscale. In this article, we discuss a quantized spin Hall response in heterostructures composed of a three-dimensional topological insulator (TI) film and a ferromagnetic normal insulator (FMNI). The magnetic proximity effect at the TI/FMNI interface provides exchange splitting of the topological states in the TI film. We predict analytically that the FMNI/TI/FMNI trilayer can be driven into the QAHE state either from the topologically trivial state or the quantum spin Hall state, depending on the TI film thickness and the interface potential. We calculate the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Our results provide a useful guide to realize the QAHE regime in the TI/FMNI heterostructures.