Dalibaltayan was born in Bogdanovka, Javakheti, Georgian SSR (present-day Ninotsminda, Samtskhe-Javakheti, Georgia). He was married to Shushanik Dalibaltayan (née Khachatryan). They have two children, a daughter Varduhi (b. 1952) and a son Varazdat (b. 1954).