Advancements in machine learning have drastically improved our ability to fit biophysical models of neural systems. We present here a fully-differentiable, biophysical model of the mouse retina that is primed for gradient-based optimization. Our model is based on the Jaxley software library (Deistler et al. 2024, Bernstein Conference) and JAX machine learning framework. The model consists of a network of Hodgkin-Huxley style neurons, realistic synapse dynamics, an experimentally-informed organization of cells in 3D space, and spatially constrained connectivity. We further implemented a wide variety of biophysical mechanisms that have been thoroughly described in the mouse retina literature such as ion channels, ribbon synapses, gap junctions, metabotropic glutamate receptors, and the phototransduction cascade. These mechanisms along with the 3D organization of neurons account for differences in the dynamics of all of the major neuron types in the mouse retina. All of these mechanisms are synthesized in our biophysically detailed model of the mouse retina to produce convincing voltage traces, but mechanisms can be left out to test various hypotheses. All implemented retinal mechanisms will be available to the community as part of the jaxley-mech library. Our retina model can be trained both to perform vision tasks and to produce the activity of single cells in experimental recordings. Our model - together with the implemented libraries - thus contributes to the advancement of multiscale neuroscience.