The Baytown Police Department said officers responded to a family disturbance at 4 a.m. on Friday at an apartment complex in the 3700 block of Garth Road.
When officers entered the apartment, they found a man armed with a knife, failing to comply with the officers' verbal orders, according to police.
The man then advanced at the officers, they said, at which point the officers shot him; the man was pronounced dead at the scene, police said.
Following the shooting, the officers searched the apartment and found a woman dead, officials said. Officers confirmed the woman was the mother of the suspect's children.
The officers then found their two children inside the apartment, took them to safety, and provided assistance, according to the department.
Baytown PD said that no officers were injured and that their homicide unit is now leading the investigation.