A woman and her two sons were found dead Saturday morning inside a Staten Island home, and her husband — the children’s father — is in custody as a person of interest, law enforcement sources said.

The 37-year-old woman and her boys, ages 2 and 3, were found shortly before 10:45 a.m. lying face down on a bed inside a two-story brick home on Palisade Street near Lily Pond Road in Arrochar, the sources said.

The children were drowned in the bathtub, law enforcement sources said. It’s unclear how their mother died.

The victims’ remains were found after one of the woman’s coworkers went to the home and discovered a small fire on the second floor, police sources said. The coworker called the FDNY around 10:35 a.m.

Just hours earlier, around 7:45 a.m., the 36-year-old husband and father was allegedly pulled from the Brooklyn side of the Verrazzano-Narrows Bridge, after bystanders saw him standing along the side of the span and called 911.

The man was taken to Maimonides Medical Center for evaluation. He has since been taken into police custody as a person of interest in the deaths, police sources said.

“We’re not looking for anyone,” a law enforcement source said.

Neighbors and law enforcement sources told The Post the husband and wife are associated with the Air Force, and U.S. Division of Military and Naval Affairs personnel were observed at the scene on Saturday afternoon.