Connolly, 80, was diagnosed with Parkinson's disease 10 years ago on the same day he found out he had prostate cancer, for which he later received the all-clear.
The comic spoke about the degenerative disease with Stephenson for an article in The Guardian.
"It's very difficult to see the progression exactly because a lot of things come and go," he said.
"Recently I've noticed a deterioration in my balance.
"That was never such a problem before, but in the last year that has come and it has stayed.
"For some reason, I thought it would go away because a lot of symptoms have come and gone away ... just to defy the symptom spotters.
"The shaking has reappeared ..."
Stephenson added: "The balance issue has been most significant, hasn't it?
"Especially since, unfortunately, it resulted in you having a couple of serious falls ..."
Connolly responded: "It's funny, that fall I had when I landed on my jaw reminded me of a thing I used to do on stage.
"I used to say: 'I fell out of bed, but luckily my face broke my fall ...'
"It's just added to the list of things that hold me back.
"I feel like I want to go for a walk, but I go for 50 yards and I want to go home because I'm tired."
Connolly said he was being "encroached upon" by the disease.
"It's creeping up behind me and stopping me doing things," he said.
"It's a cruel disease."
Stephenson said the disease had been "pretty slow-moving".
"Really, really slow-moving, but that doesn't make it any more pleasant," Connolly said.
The couple spoke about how their relationship had changed since the comedian was diagnosed.
Connolly said his wife now dressed him in the morning and that he had to "get lifts everywhere" as he "can't drive anymore".
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