There are some discrepancies between the document "Descendants of Henry Pope" by Pearl Dehlinger LaRock and the 1860 and 1870 US Census.
According to the LaRock document, Henry and Elizabeth are known to have the following children: Will, Ethel, Libby, Jennie, and Alma. Birth information is only provided for Alma, who is the youngest, and allegedly the only child born in the United States. From the 1860 and 1870 census, the known children of Henry and Elizabeth are: Henry, Elizabeth, William, Joseph, Jane and Alma. It is presumed "Will" and "Libby" from the LaRock reference is William and Elizabeth and perhaps "Jennie" is Jane. The children from both the census and LaRock document are all retained here until more information is available.
As far as birth location for the children, both the 1860 and 1870 census provide consistent information. It appears that Henry and Elizabeth must have immigrated to the United States between 1838 and 1844, between the births of Elizabeth and William. William was born in New York, with the remaining children, Joseph, Jane and Alma being born in Illinois (this also conflicts with the LaRock document, which places the birth of all children in England except Alma).