I think I have found your answer.At familysearch.org I found the marriage record for Louisa Kitchell who married Frederick Grabenstein in 1908 in Indiana.Her father is listed as Frank Croton Kitchell and her mother as Anna Martha Friday, both born in New Jersey.(Go to the above site and put in the name Louisa Kitchell and you should get a link to more complete information on the marriage.)
That didn’t make sense until I remembered that although the relationship was supposed to be to the Head of the Household, I have often found the relationship to be to the wife in the family, so I checked back.I thought that perhaps Martha was a sister of William Miller’s wife, not William.
1860 New Jersey, Warren township, Somerset Co. NJ
George Friday, 48, b. Hesse Cassel Catherine, wife, 41, b. Baden Louisa 13, b. Baden (now you know where Louisa got her name) George, 13, NJ Martha. 7, NJ Lena,7, NJ (William Miller’s wife and apparently Martha’s twin) Peter, 5, NJ Elizabeth, 5, NJ (another set of twins) Augustus, 2, NJ John, 0, NJ.
Frank Croton Kitchell was a Union veteran, serving from Indiana.