I assume you have both raster and vector in the same Coordinate Reference System (CRS).
In ArcGIS 10.2, first use Feature to Raster to convert the building vector to raster. In the
field parameter, choose the 'height' column. Try setting the cell size equal to DEM's cell size.
Then, use the Raster Calculator to add values from the 'height raster' to DEM. Something like:
"height_raster" + "DEM"
Alternatively, one can also use Cell Statistics to sum values from both rasters.
A Spatial Analyst license is required with both
Raster Calculator and