Police launched a murder investigation after a woman in her 30s and a man in his 40s were found dead in a house in Worthing, West Sussex, at 1.51 am on Friday.
They are believed to be 35-year-old Maryna Kavaliauske and Viasia Chernoff, also known as Alex, 43, a Sussex Police spokeswoman said on Sunday.
The pair knew each other, but were not related and are yet to be formally identified.
Her husband of 15 years, Giedrius described her as a "wonderful mother" to their children, aged nine and 12, and said they were a "very happy family" in a statement issued by the force.
Thousands expected to take part in 'Derry Day' this weekend
Two new arrivals in DUP camp as UUP councillor Alan Lewis defects alongside serial party-switcher Henry Reilly
Brexit: There’s a fundamental con trick being played over Liz Truss’ Northern Ireland Protocol Bill says Lord Empey
Search for missing man ends with body found on north coast
Rishi Sunak’s treasury ‘no friend of ours in fight against Protocol’: Paisley
A post mortem carried out on Saturday found Mrs Kavaliauske died from a ligature compression to the neck and Mr Chernoff died from hanging, police said.
Neighbours spoke of their shock at the deaths as forensic teams searched the home in South Farm Road, describing the family who lived there as quiet and private.
Detective Superintendent Adam Hibbert, of the Sussex and Surrey major crime team, said: "At the present time we are not looking for anyone else in connection with the investigation and our enquiries are continuing to establish the full circumstances of the deaths.
"I would discourage anyone from speculating as to what has happened as we have a distraught family with two young children trying to come to terms with their loss and to start grieving."
Anyone with information should call police on 101 quoting Operation Assert.