Programatically identifying Joined Field in ArcMap?

Here is an ArcObjects approach, based off this example, to enumerate all joins on a layer and list their destination and source table names and primary and foreign keys:

1. Get a reference to an ILayer that has one or more joins
2. Cast the ILayer to IDisplayTable
3. Cast the IDisplayTable.DisplayTable property to IRelQueryTable
4. While the current table is an IRelQueryTable:
   1. Inspect the RelQueryTable's DestinationTable and SourceTable properties
   2. Inspect the OriginPrimaryKey and OriginForeignKey properties of the IRelQueryTable.RelationshipClass property.
   3. Set the current table to the current RelQueryTable's SourceTable property

This Python script (using comtypes and this helper module) will go through all of the joins, from latest to earliest, and print the destination and source table names, origin primary key and origin foreign key for each join:

from ESRICOMHelpers import * # helper module from https://gis.stackexchange.com/a/5082/753
esriArcMapUI = GetESRIModule("esriArcMapUI")
esriCarto = GetESRIModule("esriCarto")
esriGeoDatabase = GetESRIModule("esriGeoDatabase")

def listJoins(table):
    while CType(table, esriGeoDatabase.IRelQueryTable):
        relQueryTable = CType(table, esriGeoDatabase.IRelQueryTable)
        destTable = relQueryTable.DestinationTable
        sourceTable = relQueryTable.SourceTable
        destDataset = CType(destTable, esriGeoDatabase.IDataset)
        sourceDataset = CType(sourceTable, esriGeoDatabase.IDataset)
        relClass = relQueryTable.RelationshipClass
        print destDataset.Name, sourceDataset.Name, relClass.OriginPrimaryKey, relClass.OriginForeignKey
        table = sourceTable

if __name__ == "__main__":
    #app = GetCurrentApp() # Use if run in-process
    app = GetApp("ArcMap") # Use if run in a standalone script
    mxd = CType(app.Document, esriArcMapUI.IMxDocument)

    # Gets the first layer in the active data frame
    map = mxd.FocusMap
    lyr = map.Layer[0]

    # Need to get the "display table" to access the joins
    displayTable = CType(lyr, esriCarto.IDisplayTable).DisplayTable

    # List the layer's joined tables
    listJoins(displayTable)

Example output, given a source layer with three joins:

join_table_3    master_fc_join_table_1_join_table_2    JOIN_ID_3    master_fc.MASTER_ID
join_table_2    master_fc_join_table_1                 JOIN_ID_2    master_fc.MASTER_ID
join_table_1    master_fc                              JOIN_ID_1    MASTER_ID

For more info, see How do I access ArcObjects from Python?