Jealous alcoholic Carl Mills, 28, bombarded his partner with threatening texts and, convinced she was inside with another man, warned: "I will burn your house down."
Mills stood unemotional and apparently uninterested as the jury at Newport Crown Court delivered three unanimous guilty verdicts.
He then sat and listened to a family victim impact statement read out to the court by prosecutor Gregory Bull QC.
Read: Man guilty of triple fire murder
A man has been jailed for 30 years for murdering three generations of a family in a fire.
Carl Mills, 28, will serve a minimum of 30 years after burning a family to death, including grandmother Kim Buckley, 46, her daughter Kayleigh, 17, and 6-month-old Kimberley.
The blaze ripped through the family home in Coed Eva, Cwmbran, south Wales, in the early hours of September 18, last year.