The Irish actor, 38, walked their pet dog as American star Caitlin, also 38, pushed the black stroller.
The couple were reported to have welcomed their first child into the world back in January, but have not publicly confirmed the news themselves.
While the married stars have been keeping a low profile ever since, they have been seen out and about with a pram on a couple of occasions.
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Caitlin was bundled up for the British weather as she donned a number of layers for her outing in the early spring sunshine.
Wearing a mink-coloured cardigan, a khaki jacket, and a blue neck scarf, the Masters of Sex actress finished off her look with a pair of black sunglasses, jeans and trainers.
The star opted to wear her blonde tresses in a loose natural style, and appeared deep in conversation with her beau as they strolled along the pavements in East London.
Aidan meanwhile, didn’t appear affected by the chill in the air and opted for a plain navy T-shirt and black jeans for the walk.
The star was sporting a thick bushy beard as he grinned and chuckled with his wife.
The couple also seemed to have taken a trip to the shops as they had some bags in the bottom of the pram.
Aidan and Caitlin were said to have married in a secret Italian wedding in August 2020.
The nuptials didn’t come to light until nearly a year later, in March 2021, as it was reported that they chose to have their big day during the pandemic, but without guests, as they “didn’t want to wait” any longer.
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The couple first started dating in 2017 after filming The Man Who Killed Hitler And Then The Bigfoot, according to reports, before getting engaged in 2018.
Last year, a source spilled on their nuptials as they told The Sun: “The couple are both madly in love and couldn’t wait to get hitched when their schedules allowed.
“They’re both very private and have kept the ceremony very much under wraps, but he has been seen taking lockdown walks with his wedding ring on show.”
The source continued: “Aidan hasn’t been in a rush to get wed and has very much been waiting for ‘The One’ to come along – and anyone who sees them knows they’re the perfect match.”
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