Not sure what the Patch Analyst is, but you could indeed convert the raster to polygons and use a union to create a featureclass with all the combinations (habitats vs counties). Then you can join the areas of the original counties to the result and determine the percentage for each habitat x county combination.
If you have access to Spatial Analyst you could also do this in raster format. The tool that you would need is the Combine tool. The resulting raster has an attribute table with the combinations (a unique value will be created for each unique combination of habitat and county).