Transmission of information using the spin of the electron as well as its charge requires a high degree of spin polarization at surfaces. However, at surfaces this degree of polarization can be quenched by competing interactions. Using a combination of surface-sensitive X-ray and tunnelling probes, we show for the quasi-two-dimensional bilayer manganites that only the outermost Mn-O bilayer is affected: it is a 1-nm-thick insulator that exhibits no long-range ferromagnetic order, whereas the next bilayer displays the full spin polarization of the bulk. Such an abrupt localization of the surface effects is due to the two-dimensional nature of the layered manganite, and the loss of ferromagnetism is attributed to weakened double exchange in the reconstructed surface bilayer and a resultant antiferromagnetic phase. The creation of a well-defined surface insulator atop a fully spin-polarized bulk demonstrates the ability of two of the most demanding components of an ideal magnetic tunnel junction to self-assemble naturally.