Neighbours say they believe that the home belongs to a housing association.
One local resident, who asked not to be named, said: "The eldest, their daughter, is about seven or eight - she knocked on the neighbour's door.
"There's a small baby and another child. The children were taken out. One of them, the middle child, was refusing to come out initially, as they wanted to stay inside with their mother."
A woman living down the road said: "He [Lander] was a lorry driver and was away a lot.
'I don't know her name but she looked quite harassed a lot of the time with three kids to look after. It's terribly sad what has happened, especially in front of their children."
The three children, who are all under the age of eight, are being cared for by family members.
West Midlands Police Detective Inspector Jim Munro confirmed that police are not looking for anyone in connection with the deaths.
Detective Inspector Munro said: "This is a truly tragic incident. It's understood the woman was violently attacked before the offender took his own life.
"The timeline of exactly what happened is unclear but we believe the two people died during the morning.
"There were three children, including a small baby, present at the address when officers made the discovery - they are being looked after by loved ones and will receive specialist support."
Post-mortem examinations will take place later on Monday, police said.
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