'The Last Post' actor - who married 'The Crown' star in 2014, with whom he shares a two-year-old daughter - had the benign tumour on his pituitary gland, at the base of the brain, removed at the end of 2016, while Claire was busy filming the second season of the Netflix series.
Looking back, Stephen admits the scare put his family through hell and back, and he also shared how he wrote a letter just in case he didn't make it through the operation.
Stephen, 38 - who is now in recovery - said: ''You realise you're not the most important person in that process, and everybody who loves you goes through far worse.
''My daughter didn't know what was going on at all. But my family did and I could see it in them.''
He added: ''There are certain things that you make sure you've done before you go into surgery.
''You write a letter. But it's all very much on the off chance that something did go wrong, because every part of you is saying that nothing will. 'Waking up and being told the operation had gone well was understandably a huge relief.''
Meanwhile, Claire herself has revealed she battled a ''horrible and debilitating'' tumour in her eye when she was just 17.
The 33-year-old Golden Globe-winning actress told The Sun newspaper: ''It was horrible and debilitating, but it made me realise that I needed to grab the life I wanted. If that hadn't happened, I don't know if I would have been brave enough to throw my cards on the table and say I wanted to study drama.''
She added: ''I'm quite lucky to have a face. I was a bit like Cyclops and it was all a bit scary. I was on steroids for about a year and a half afterwards that makes you put on a lot of weight and have really bad skin.''
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