We demonstrate that the structure of the outermost orbitals of oxygen and nitrogen can be observed in the angular distribution of coincident ion pairs generated by the double ionization of these molecules by 8 fs laser pulses. We do this by establishing that these ions emerge from well defined excited electronic states of O2+2 and N2+2 respectively and that they are produced dominantly through a process which involves electron rescattering. The angular distributions of the ions from the two targets are very different, reflecting the different structures of the outermost orbitals of the two molecules.