Extracting raster DEM elevations to vector attribute tables in ArcGIS Desktop?

I have an ArcMap 10 project with multiple layer groups. One layer is a raster DEM, another layer group is a bunch of vector shapefiles (including points, lines and polygons). The client wants all vector data to contain Z values.

Populating the attribute tables for the vector data with X and Y values is easy enough but how do I populate the Z values?

Is there a way that I can use Field Calculator to "grab" the height values from the DEM layer for each vector feature?

I should add that we don't have a licence for the 3D Analyst or Spatial Analyst extensions.