Biswas was first married for love, and much against the wishes of his own family, a Muslim actress who was four years older than him. This was Mehrunnisa (born 17 October 1910, died 1992), who had adopted the screen-name 'Ashalata' for work purposes. Upon her marriage, Mehrunnisa assumed the name Ashalata as her one and only name. Ashalata worked as an actress during the 1930s and 1940s, a period during which acting in films was considered disreputable and few women entered the industry; she also owned Variety Pictures, a film-making company. The couple became the parents of three sons and a daughter, named Pradeep, Amit, Utpal and Shikha. Their son, Utpal Biswas, also worked as a music composer, as part of the Amar-Uptal duo team which composed the music for a few films including "Shahenshah" (1988), "Main Azaad Hoon" and "Aaja Meri Jaan" (1993). Biswas's daughter, Shikha Vohra, is the mother of the well-known documentary film maker, Paromita Vohra. Biswas and Ashalata were divorced in 1954; Ashalata Biswas died in 1992.