He married Joan, daughter of Richard de Arundel, Knt., 10th Earl of Arundel, 9th Earl of Surrey, and his 2nd wife Eleanor of Lancaster. (Humphrey's sister Elizabeth married Joan's brother Richard, 11th/4th Earl.) A papal dispensation for the marriage, required because they were related in the 4th degree, was dated 9 September 1359, and the license for the marriage was dated 17 October 1359.
In 1360 he succeeded his father as Earl of Northampton. On 15 October 1361 he succeeded his father as Earl of Hereford and Essex and Constable of England.
In November 1363 he headed an escort of King Peter I of Cyprus from Dover to London. In 1367 he crusaded with King Peter in the Levant. He was back in London by May 1368.
He was made a Knight of the Garter in 1365. He was appointed chief Ambassador to Milan in 1366. He undertook diplomatic missions in 1366 and 1367, and headed an Embassy to the Duke of Brittany in 1371.
In 1369 "he had command in the expedition against France" with John of Gaunt.
Humphrey died on 16 January 1372/3 and was buried at Walden Abbey, Essex. His daughters Eleanor and Mary were coheirs of his vast estates.
Humphrey's will, dated 12 December 1372, was proved 15 May 1373. His widow, Joan, died in 1419.
There is no mention of a daughter of Humphrey de Bohun and Joan Fitzalan called Elizabeth in the works of Douglas Richardson, nor in Medieval Lands, nor in T Anna Leese's Blood Royal. The Wikipedia article on her father lists a daughter Elizabeth who died young. Some family trees on the internet include Elizabeth without giving sources. It would be good to find more evidence for her existence. - Michael Cayley, 24 March 2019
Contrary to what is said on Wikipedia, Humphrey appears not to have participated in the sack of Alexandria in Egypt in 1365: it was only in 1367 that he joined Peter I of Cyprus's crusading forces.
Some websites wrongly suggest that, as he had no son, Humphrey's estates should have passed to his cousin Gilbert de Bohun, and that it was royal intervention which led to them passing between his daughters. This shows a lack of understanding of the laws of feudal inheritance, under which his daughters were entitled to share the estates.
The Walden Cartulary gives a different date of death of 16 Feb 1372.
↑ Douglas Richardson. Royal Ancestry: A Study in Colonial and Medieval Families, 5 vols, ed. Kimball G. Everingham (Salt Lake City: the author, 2013), volume I pages 426-427 BOHUN 11.
↑ Monasticon Anglicanum. By Sir William Dugdale, Knight. Vol. 4. London, 1846, p140. 
Richardson, Douglas. Royal Ancestry: A Study in Colonial and Medieval Families, 5 vols, ed. Kimball G. Everingham. Salt Lake City: the author, 2013. See also WikiTree's source page for Royal Ancestry.
Richardson, Douglas. Magna Carta Ancestry: A Study in Colonial and Medieval Families, 4 vols, ed. Kimball G. Everingham. 2nd edition. Salt Lake City: the author, 2011. See also WikiTree's source page for Magna Carta Ancestry.
Cokayne, G E. Complete Peerage, revised and enlarged, Vol. VI, St Catherine Press 1926
Leese, T Anna. Blood Royal, Issue of the Kings and Queens of Medieval England 1066-1399, Heritage Books 2007, pp. 89, 114-115 and 170-1