In this paper, we propose a two-stage heterogeneous lightweight network for monaural speech enhancement. Specifically, we design a novel two-stage framework consisting of a coarse-grained full-band mask estimation stage and a fine-grained low-frequency refinement stage. Instead of using a hand-designed real-valued filter, we use a novel learnable complex-valued rectangular bandwidth (LCRB) filter bank as an extractor of compact features. Furthermore, considering the respective characteristics of the proposed two-stage task, we used a heterogeneous structure, i.e., a U-shaped subnetwork as the backbone of CoarseNet and a single-scale subnetwork as the backbone of FineNet. We conducted experiments on the VoiceBank + DEMAND and DNS datasets to evaluate the proposed approach. The experimental results show that the proposed method outperforms the current state-of-the-art methods, while maintaining relatively small model size and low computational complexity.