Two days after a man in a mask knocked on their door, identified himself as a police officer and opened fire on them, John and Yvette Hoffman are recovering and "both incredibly lucky to be alive," their family said in a statement.

"We continue our healing journey and are humbled by the outpouring of love and support our family has received from across the state and our nation," the family said in a statement obtained by ABC News.

The couple said they had "deep and profound" gratitude for the work of law enforcement officials who tracked down the suspect, Vance Boelter, 57, after Friday's shooting.

Boelter is alleged by law enforcement to have shot and killed Minnesota state Rep. Melissa Hortman and her husband, Mark, and shot and injured the Hoffmans, according to documents obtained by ABC News.

Boelter has been charged with two counts of murder and two counts of attempted murder, with the second set of charges related to the shooting at the Hoffman's house. He's due in court on Monday.

Court records filed in Hennepin County, Minnesota, say that the child of a state legislator initially made the call at 2:05 a.m. that their parents had been shot.

"Defendant knocked on the door and announced himself as a police officer before entering the house and shooting Victims 3 and 4," according to court documents. Based on court records, it is believed that the Hoffmans are Victims 3 and 4.

The Hennepin County Attorney said that because a state legislator was shot police proactively went to another state legislator's house -- that of Hortman, who was a former speaker.

"When officers arrived at approximately 3:35 a.m., they saw the Ford SUV with police-style lights and immediately saw Defendant, still dressed as a police officer, shoot an adult man referred to herein as Victim 2 through the open door of the home," according to court records.

When officers searched Boelter's vehicle, they allegedly found at least three AK-47 assault rifles, a 9mm handgun, as well as a list of names and addresses of other public officials.

The Hoffman family in their statement said there was "never a place for senseless political violence and loss of life."

"We are devastated by the loss of Melissa and Mark, and our hearts go out to all those who knew and loved them both," the statement. said. "We are always at our best when we unite together."

ABC News' Darren Rynolds and Jessica Gorman contributed to this report.