He is married to Margaret Skinner.
They got married on January 16, 1584 at Warfield, Berkshire, England, Great Britain.
Child(ren):
http://www.british-history.ac.uk/no-series/london-aldermen/hen3-1912/pp168-195
1556.James Altham. Son of Edward Altham, Sheriff 1531– 2. His first wife was sister of Sir Thomas Blanke (Lord Mayor 1582– 3) and his second was daughter of Sir Andrew Judde (Lord Mayor 1550– 1). By the former he was father of James Altham, Baron of the Exchequer, whose daughter married Arthur Annesley, first Earl of Anglesey. Altham was fined 100 marks 'for his contemptuous disobedyence in not observynge the order of this Court' [Rep. 14. fo. 513b] July 24, 1561, and discharged from his Aldermanry a week later.
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https://en.wikipedia.org/wiki/James_Altham
He was the third son of James Altham of Mark Hall, Latton, in Essex, Sheriff of London in 1557, and sheriff of Essex in 1570, by Elizabeth Blancke, daughter of Thomas Blancke of London, haberdasher, and sister of Sir Thomas Blanke, who was Lord Mayor of London in 1583.