I did some searching for you and found some things. I'm not related to the family, just helping out.
His father's name was Edwin T Miller, born about 1818 in Kentucky. His mother was Angeline Johnson, born about 1819 in Kentucky. They were married 19 Mar 1835 in Shelby County, Kentucky. The marriage record has Angeline's father as Benjamin J Johnson. I found the marriage record on familysearch.org in "Kentucky Marriages, 1785-1979". You can go there and see it and make a copy if you would like.
On the 1850 census they were in Spencer County, Kentucky.
I found Barnett's death record on Ancestry.com and it had his parents as Edward and Evangeline Miller, but that was not quite correct. The death record was from Butler County, Kentucky and said Barnett died 10 Feb 1907 of kidney trouble. The record had him listed as B J Miller.
On the 1860 census they do have Edwin listed as Edward and they are in Daviess County, Kentucky at this time and Angeline is listed as Angelina. On the 1870 census they are still in Daviess County, Kentucky. On the 1880 census they are in Ohio County, Kentucky. It has Edwin's parents as being from Virginia, Angeline's parents from Kentucky.
That's about all I have found for now. Hope this helps out.