We use x-ray emission spectroscopy to elucidate the molecular structure of liquid methanol, water, and methanol-water solutions. We find that molecules in the pure liquid methanol predominantly persist as hydrogen-bonded chains and rings with six and/or eight molecules of equal abundance. For water-methanol solutions we find evidence of incomplete mixing at the microscopic level. Our results provide a new explanation for a smaller entropy increase in the solution due to water molecules bridging methanol chains to form rings.