The imaging fidelity of mesoscopic fluorescence molecular tomography (MFMT) in reflective geometry suffers from spatial nonuniformity of measurement sensitivity and ill-posed reconstruction. In this study, we present a spatially adaptive split Bregman network (SSB-Net) to simultaneously overcome the spatial nonuniformity of measurement sensitivity and promote reconstruction sparsity. The SSB-Net is derived by unfolding the split Bregman algorithm. In each layer of the SSB-Net, residual block and 3D convolution neural networks (3D-CNNs) can adaptively learn spatially nonuniform error compensation, the spatially dependent proximal operator, and sparsity transformation. Simulations and experiments show that the proposed SSB-Net enables high-fidelity MFMT reconstruction of multifluorophores at different positions within a depth of a few millimeters. Our method paves the way for a practical reflection-mode diffuse optical imaging technique.