arcgis desktop - Calculate raster statistics per polygon in a polygon feature class

I have a raster layer representing land cover which has three categories of pixels: natural, semi-transformed and transformed.

I have a polygon feature class where each polygon delineates a catchment area.

I would like to calculate the proportion of each of the land cover types in each polygon. For example: I would like to know what percentage of each polygon is natural, semi transformed and transformed. I would like this information to be contained in the attribute table of the polygon feature class.

I am using ArcView License, ArcMap 10.0. I have the 3D Analyst Extension but not Spatial Analyst.