The field-emission tunneling barrier has been mapped for the doublet and quadruplet emission patterns associated with organic adsorbates on tungsten. The tunneling barrier was mapped by photometric probe-hole field-emission electron microscopy (PhotoFEEM). The adsorbates were deposited by evaporating a film of the molecule copper-phthalocyanine (CuPc) but it may be polymeric groups of CuPc or decomposition products. The tunneling barrier displays unexpected structures that are not seen in the corresponding field-emission images. Doublet patterns observed in the FEEM image can display singlet structures in the corresponding PhotoFEEM barrier maps. Similarly, quadruplet patterns in the FEEM image can display doublet structures in the PhotoFEEM barrier maps. This behavior is similar to supply limited tunneling previously observed in the Field-emission barrier of a clean tungsten emitter. An analysis of deviations from purely linear Fowler-Nordheim behavior indicates that the observed structures arise from independent emitters hat are spatially superimposed on the surface.