I can think of a couple of approaches to this. The simplest one is to calculate the difference between your buffers and the envelope of your area of interest. Have a look at the Erase and Symmetrical Difference Tools in the Analysis Toolbox. Your problem here though, is that they are available only with the ArcInfo licence. ETGeoTools might have something but I don't recall any useful function in the free version. QGIS can accomplish the task for free though.
A simple work-around for ArcGIS if you don't have the ArcInfo licence, is to create your envelope polygon and then Union it with your buffers. From the result of that operation, select all the polygons that are identical to you buffer areas and delete them. Everything left is your "inverted buffers".