Curriculum learning begins to thrive in the speech enhancement area, which decouples the original spectrum estimation task into multiple easier sub-tasks to achieve better performance. Motivated by that, we propose a dual-branch attention-in-attention transformer dubbed DB-AIAT to handle both coarse- and fine-grained regions of the spectrum in parallel. From a complementary perspective, a magnitude masking branch is proposed to coarsely estimate the overall magnitude spectrum, and simultaneously a complex refining branch is elaborately designed to compensate for the missing spectral details and implicitly derive phase information. Within each branch, we propose a novel attention-in-attention transformer-based module to replace the conventional RNNs and temporal convolutional networks for temporal sequence modeling. Specifically, the proposed attention-in-attention transformer consists of adaptive temporal-frequency attention transformer blocks and an adaptive hierarchical attention module, aiming to capture long-term temporal-frequency dependencies and further aggregate global hierarchical contextual information. Experimental results on Voice Bank + DEMAND demonstrate that DB-AIAT yields state-of-the-art performance (e.g., 3.31 PESQ, 95.6% STOI and 10.79dB SSNR) over previous advanced systems with a relatively small model size (2.81M).