Since Jonathan and Eliza are listed as black in the 1870 census, and white in the 1880, my experience tells me that they may have been Indians. Blacks were pretty much always listed as black, whites, as white. Only Indians seemed to "change"race depending on the area they lived since they didn't fall within the two main categories.
I'm having difficulty finding this couple on the 1850 census. According to the 1860 census, they should have been in TN by then. Any clues?
By the way, there are Hulans on the Dawes Rolls, but that was around the turn of the century, and to check that out, I would need more info on other down-lines of the male Hulens.