None of Bard’s family is mentioned in the book. However we know from Frodo’s conversation with Gloin in Rivendell (The Fellowship of the Ring – Many Meetings) that Brand, son of Bain, son of Bard rules the people of Dale at the time of the Fellowship’s journey. So, we know that Bard married and had at least one child, his son Bain, and that he in turn married and had a son. From The Tale of Years (Appendix B to The Lord of the Rings), we know that Bain succeeded his father Bard, as Lord of Dale in year 2977 of the Third Age. It was during his rule, which lasted 30 years, that Balin took a group of dwarves to re-establish their realm in Moria.
In year 3007 of the Third Age, Bain was succeeded as King of Dale by his son Brand. Brand ruled Dale during the time of the War of the Ring. At the same time Minas Tirith was besieged (March of the year T.A. 3018) servants of Sauron attacked Dale. There was a great battle at the foot of the Lonely Mountain that lasted three days. In the end, both Brand and Dain Ironfoot were slain and Erebor lay under seige. Finally, Bard II and Throin III drove the enemy away and, presumably, Bard II then became the next King of Dale .
Bain appears in the last two movies of the Hobbit trilogy. In the movies, he as two sisters: Sigrid and Tilda. Their mother passed away before the time of the movies, but nothing is said about the manner of her death. At the time of The Hobbit movies, Bain is in his early teens. The actor, John Bell, who play Baindescribes his character as: “a young boy ready to do battle when needs be and to protect his father.”