Arlington police say the couple allegedly had argued over child support issues.
Arlington City Jail records show 29-year-old Thomas Olivas of Bedford was being held Tuesday on a capital murder charge. Bond has been set at $1 million for Olivas, who was arrested Monday night at a bar in Hurst.
Officials say 26-year-old Mechelle Gandy had been stabbed and she died at the scene of the fire at her Arlington apartment. Her son, Asher Olivas, died as a result of the March 20, 2011, blaze.
Jail records did not list an attorney for the defendant.