Layered nanoscale amorphous solid films of methanol and ethanol undergo complete intermixing prior to the onset of measurable desorption at 120 K. This intermixing precedes and inhibits crystallization. Subsequent desorption of the film is described quantitatively by a kinetic model describing evaporation from a continuously mixed ideal binary liquid solution. This occurs at temperatures below the melting point of the binary mixture, indicating ideal behavior for the supercooled liquid solution. This approach provides a new method for preparing and examining deeply supercooled solutions.