Mapping Center Answer:

The only way to do this is to create a join for that feature class, when you use it as a layer in ArcMap, to the table containing the text you want to label. We have a help topic that covers this procedure: Appending related fields with a join.

I’ve done a bit of work with soils data (U.S. Soil Conservation Service) and their data model has a base feature class with 50+ relate-able tables. I ended up writing Python scripts to perform the joins I needed for displaying various types of information on maps, that way I could just run a script and get exactly the data I needed for a given map. An additional advantage is that the institutional knowledge for how to process the data for that map is now captured in a script.