Detective Constable Sheila Farquharson was giving evidence at the trial of Tony Vita, 47. He denies stabbing wife Marion to death at Barrachnie Crescent, Baillieston, Glasgow on September 20 last year.
In the police interview Mr Vita said he had been married for 19 years and known his wife for 20 years. They met at work at the Department of Work and Pensions.
DC Farquharson said Vita claimed to have had a good relationship with his wife but said they had a trial separation four months earlier.
Mr Vita said his wife was tired as she worked full-time at Edinburgh's Crown Office and was studying for a degree. Asked if she was in a relationship with a woman named Elwira Rumniak he replied: "No comment."
He was also asked if his wife ever stayed with Miss Rumniak and said: "Not as far as I was aware."
But the jury heard an entry on his kitchen calendar for September 19, 2013 read: "Marion = cheating lesbian whore."
Asked by advocate depute Douglas Fairlie QC : "At any time did you notice any sign of grief or upset about his wife's death?" DC Farquharson replied: "No, none."
When Mr Vita was asked if he had murdered his wife he told police: "No comment."
Detective Sergeant Andrew Gibson confirmed a letter written by Mr Vita addressed to his father was found at the crime scene.
The letter said: "Dear dad, I'm very sorry for what I've done. I have been unhappy for months. I only found out yesterday that Marion has had an affair with Elwira."
The trial continues.