What is the proper description/name of this amide/ester structure?
In IUPAC speak it is a carbamic acid methyl ester. 

The IUPAC name for the compound drawn according to Chemspider structure search is Carbamic acid, N-[5-(propylthio)-1H-benzimidazol-2-yl]-, methyl ester  1

Most working chemists would call it a methyl carbamate