I was just wondering about the Henry I found for you.. If he was Irish/white then maybe he was just listed as mulatto/black in census because he was married to a black woman??
You said the names of children sounded familiar so I think it possible this is the right Henry.You said he was aslave though and I don't think I have heard of any white slaves??, but if one of his parents was black then maybe he was considered black? I am jut throwing out ideas as he is a bit of a mystery.
Also if he was a slave it is possible that his name was different at that time. Also if he was a slave it would have been as a child as slavery ended after the Civil War - or was supposed to anyway.
But if this is the right Henry then he was born about 1853 and could easily have been a slave through the end of the War when he would have been about 12-13 years old.
Also if it is the right Henry he was born NC(according to 1900 census)so I am going to look at the slave schedules but as you know most of them don't have the names of the slaves- only of the owners but I'll look just in case something comes up. Maybe a slave owner named Higgs (some slaves took names of their owners from what I understand)
I'll also look for the 1930 census for you for Lizzie and kids and get back to you with that soon.