The West End star told Closer magazine that things were "on track" with his wife but said that life with three-year-old daughter Betsy was sometimes tough.
He said: "Things are good and on track. Like any couple with a young child it's tough, but we're in a great place right now and any rumours to the contrary are just not true. We're together and very happy."
Denise, 38, recently revealed there had been pressures on her four-year marriage as Lee, 32, had been in the US looking for TV and film roles while she worked on 'Strictly Come Dancing'.
Lee said: "Den was doing Strictly over Christmas and I was in panto until the end of January. Then I headed out to LA for the whole of March.
"You can't just go to LA and expect the jobs to come to you. No one knows who I am there and I'm not expecting it to happen overnight.
"I missed my family, obviously. But it's part of the job. If I was to land a part in a film then I could be away for two or three months at a time. It would be very hard, but that's what actors go through."
Lee said the family were definitely in a strong position despite their time apart for work: "My family is definitely my proudest achievement - it's all about me, Den and Betsy."