I don't think that the Emancipation book will help you here. A few questions first, though. When did Simon Barnhill die, and who filled out the death information on the certificate? How sure are you that Simon's mother was actually a Barnhill who was still alive in 1870 or 1880? Do you know if Willis Whitehurst was supposed to be married to Simon's mother, or not? And how sure are you that Willis W. was actually Simon's father?
WILLIS WHITEHURST was married to JANE WHITEHURST in Pitt Co.,NC in 1859 ("Somebody Knows My Name,Marriages of Freed People in North Carolina,County by County", by Barnetta McGhee White).
You found SIMON BARNHILL in 1880, and taking a look at it, is really strange. Notice the ages of Simon (28) and notice the way the people listed as his "children" are very odd:
1880 Pitt Co.,NC, Pactolus, Image 47,#456/430
SIMON BARNHILL - Age - 28
BASHA - 35
MARTILDA - 9
ANNIE - 16
HARRY - 6
WILLIAM - 5
GEORGE - 18
He would have had to have been 10 years old to have fathered GEORGE!
So, I'm not so sure about the info in this census. But using that age as a guide, he would had to have been born about 1850 or before, which means that he was born before Willis married Jane. Since both Willis & Jane were apparently slaves because their marriages are recorded with the CoHabitation Records and there is no sign of them prior to 1870, Simon may have been a Barnhill simply from taking the name after slavery was over. That's why I'm wondering if there was actually someone who knew that Simon's mother was a Barnhill, or if someone who filled out the death certificate may simply assumed that was her surname since it was Simon's.
In looking at Willis Whitehurst's census in 1870, there is another strange set of records,and here is what we have:
1870 Pitt Co.,NC, Belvoir, Image 36 & 37,#292/312:
WILLIS WHITEHURST - 56 - B - FARMING - NC
ADLINE - 30 - B - NC
HANNAH - 7 - B - NC
SARAH - 5 - B - NC
(the race for this family was originally listed as "W", but was crossed out, and written over)
WILLIS WHITEHURST - 54 - B - FARMER - NC
ADLINE - 20 - B -KEEPING HOUSE -NC
HANNAH - 7 - B - NC
SARAH - 4 - B - NC
ROBT KNIGHT - 24 - B - NC
JANE - 20 - B - NC
ANN ROBT. - 2 - B - NC
WILLIAM H. - 1 - B - NC
Apparently this family was enumerated twice, with different ages, to boot. I don't see Simon Barnhill in this census at all, but again, he could be under a different name somewhere. You might need to try a first name search for him, or checking the neighbors he was living around in 1880 and comparing the names.
As for MARY BARNHILL, here's a thought. Assuming ADLINE was his wife, Willis W. was apparently newly remarried by 1870, the child SARAH,showing born about 1866. Perhaps she was the last child with his wife, JANE, who would have had to been alive at the time of their marriage being recorded, which was between 1865 -1866 (Ms. White indicates that the Pitt Co. cohabitation records were within a book at the North Carolina State Archives entitled, "Colored Marriages 1840-1866", and slavery ended in 1865). It's very probable that his wife died shortly after that record was made.
One of the names I've seen used for the name MARY, was JANE. Perhaps JANE WHITEHURST was SIMON BARNHILL's mother. Many times I've seen people listed as MARY, one year, JANE the next, MARY JANE, another. And some others are MARIAH,MARIA, MARIE, POLLY, MOLLY, MARTHA, MARISSA, MARYANNE, MARIANNE or MARIANE, PATSY.