The ability of proteins and other macromolecules to interact with inorganic surfaces is essential to biological function. The proteins involved in these interactions are highly charged and often rich in carboxylic acid side chains1-5, but the structures of most protein-inorganic interfaces are unknown. We explored the possibility of systematically designing structured protein-mineral interfaces, guided by the example of ice-binding proteins, which present arrays of threonine residues (matched to the ice lattice) that order clathrate waters into an ice-like structure6. Here we design proteins displaying arrays of up to 54 carboxylate residues geometrically matched to the potassium ion (K+) sublattice on muscovite mica (001). At low K+ concentration, individual molecules bind independently to mica in the designed orientations, whereas at high K+ concentration, the designs form two-dimensional liquid-crystal phases, which accentuate the inherent structural bias in the muscovite lattice to produce protein arrays ordered over tens of millimetres. Incorporation of designed protein-protein interactions preserving the match between the proteins and the K+ lattice led to extended self-assembled structures on mica: designed end-to-end interactions produced micrometre-long single-protein-diameter wires and a designed trimeric interface yielded extensive honeycomb arrays. The nearest-neighbour distances in these hexagonal arrays could be set digitally between 7.5 and 15.9 nanometres with 2.1-nanometre selectivity by changing the number of repeat units in the monomer. These results demonstrate that protein-inorganic lattice interactions can be systematically programmed and set the stage for designing protein-inorganic hybrid materials.