Hopefully, George's death record indicates who his parents were. His obituary may or may not indicate his parents, but it might at least have his siblings listed. Julia's death certificate should have her parents' names. The death certificates and obituaries of Julia's children should confirm her maiden name.
George served in Company A, 144th Indiana Infantry Regiment. He and his widow Julia received a Civil War pension: Appl. 658,440 Cert. 424,253 Widow Appl. 830,873 Cert 672,741.
You can get a copy of his pension from the National Archives in Washington, DC for $75. While a bit pricey and the genealogical data it contains is uncertain, it may have some of what you are looking for. Julia would have had to prove she was legally married and often the pensions give details about the applicants' lives that cannot be found anywhere else. As I understand all the pensions will eventually be online, but I don't know the timeline. Some are already available online at Footnote.com for a fee.