It as the same heritage as 

the Eastern Catholic Churches (Eastern Orthodox)
and
the Western Catholic Church (Roman Catholic)

but it is ecumenical in that it believes in working closely with all Christians to put Christ Jesus back into the ailing society of our modern world.

The Old Catholic Church

The  House of Bishops:

Within the Old Catholic Communion,  the Province of St. Thomas is affiliated with the Old Catholic Communion of North America. Its Bishops and Priests, as in all Catholic Churches, have been ordained in Apostolic Succession.  The Most Rev. Dr. Robert W. Burgess traces his succession directly back to Saint Thomas the Apostle.

Information about the Old Catholic Communion of North America, it's Bishops, Synod, Canon, Seminary and Clergy requirements can be found at  OCCNA - Old Catholic Communion of North America