Burnham has a brother, Nick, who is the principal of Cardinal Newman College, Preston. Burnham married Marie-France van Heel, who is Dutch, in 2000, having been in a relationship since university. The couple have a son and two daughters. Burnham was brought up as a Roman Catholic. In the 2015 leadership contest he praised Pope Francis, but urged him to promote a progressive stance on gay rights. In a newspaper interview during the contest he stated that he had been repeatedly at odds with the Catholic Church all the time that he had been an MP and that this had resulted in strained personal relationships.