On 21 October 1710, Ashburnham married Lady Mary Butler (died 1713), the second daughter of James Butler, 2nd Duke of Ormonde. After her death, he married, on 25 July 1714, Henrietta, Dowager Countess of Anglesey and 4th Baroness Strange; they had one child, Henrietta (c.1716--1732), later 5th Baroness Strange.
Henrietta
Dowager Countess