Am sure that you have noted in the 1870 census that Mary's mother, Johana O'Brien, aged 49, is likely living in the same household, along with Mary's siblings, Emma, aged 24, born Ireland; William, aged 16, born LA; and Kate, aged 14, born LA.
Andrew is in New Orleans already in the 1860 census, seemingly unmarried, and working as a grocer, with a clerk and a servant living in the same household. He and Mary were married on 30 May 1862 -- the church marriage record (if one exists) will provide good information.
Andrew died 31 May 1889, aged 53. Getting a copy of his death record may provide more information. Andrew was naturalized on 30 October 1860 in Orleans Parish in the US Circuit Court. Again, the full record may be useful.