Total internal reflection fluorescence microscopy (TIRF) produces 2D images of the fluorescent activity integrated over a very thin layer adjacent to the glass coverslip. By varying the illumination angle (multi-angle TIRF), a stack of 2D images is acquired from which it is possible to estimate the axial position of the observed biological structures. Due to its unique optical sectioning capability, this technique is ideal to observe and study biological processes at the vicinity of the cell membrane. In this paper, we propose an efficient reconstruction algorithm for multi-angle TIRF microscopy which accounts for both the PSF of the acquisition system (diffraction) and the background signal (e.g., autofluorescence). It jointly performs volume reconstruction, deconvolution, and background estimation. This algorithm, based on the simultaneous-direction method of multipliers (SDMM), relies on a suitable splitting of the optimization problem which allows to obtain closed form solutions at each step of the algorithm. Finally, numerical experiments reveal the importance of considering the background signal into the reconstruction process, which reinforces the relevance of the proposed approach.