I looked at the 2011 Ethiopia questionnaire and there is indeed no field for Zone and there is no information at the zonal level in the data files. Lower level geographical information is often not included in the questionnaire when HIV-status information is collected. However, I do believe that GIS information was collected for each cluster. The GIS information is generally scrambled to a certain extent, that means that the exact location of the cluster is randomly offset by a few kilometers, so even using the GIS information you can not be sure that exact location of the cluster falls within a certain zone.

Sorry that we can not be of more help.