Structured Illumination Microscopy (SIM) is an imaging technique for achieving both super-resolution (SR) and optical sectioning (OS) in wide-field microscopy. It consists in illuminating the sample with periodic patterns at different orientations and positions. The resulting images are then processed to reconstruct the observed object with SR and/or OS. In this work, we present BOSSA-SIM, a general-purpose SIM reconstruction method, applicable to moving objects such as encountered in in vivo retinal imaging, that enables SR and OS jointly in a fully unsupervised Bayesian framework. By modeling a 2-layer object composed of an in-focus layer and a defocused layer, we show that BOSSA-SIM is able to jointly reconstruct them so as to get a super-resolved and optically sectioned in-focus layer. The achieved performance, assessed quantitatively by simulations for several noise levels, compares favorably with a state-of-the-art method. Finally, we validate our method on open-access experimental microscopy data.