CuSn⁡(OH)6 is a quantum spin system from the family of magnetic double perovskite hydroxides, having a frustrated magnetic sublattice. It is also known as the natural mineral mushistonite, whose crystal structure has remained elusive for decades. Here we employ x-ray and neutron powder diffraction to solve the crystal structure of CuSn⁡(OH)6 and propose a structure model in the orthorhombic space group 𝑃⁢𝑛⁢𝑛⁢𝑛 with correlated proton disorder. The occupation of the hydrogen sites in the structure is constrained by “ice rules” similar to those known for water ice, albeit with only local correlations. The resulting frustration of the hydrogen bonding network is likely to have a complex and interesting interplay with the strong magnetic frustration expected in the face-centered magnetic sublattice. Structural distortions, which are quite pronounced in Cu2+ compounds due to the Jahn-Teller effect, partially alleviate both types of frustration. We also show that hydrostatic pressure tends to suppress proton disorder through a sequence of proton-ordering transitions, as some of the split hydrogen sites merge already at 1.75 GPa while others show a tendency toward possible merging at higher pressures.