One of the cards reads: "Mary just needs to admit she slept with someone else".
Another card says "Sorry your December birthday is overshadowed by a bloke that wore socks with sandals".
The owner of Love Layla said the company does not set out to upset anyone.
Stacey Dennis said: "We've really pulled out all the stops for this year's Christmas range as this is what our customers want with some designs providing much more of a playful edge.
"And with the way this year has panned out, people are in real need of a laugh and a giggle.
"Christmas isn't just about religion it's also about having fun and enjoying ourselves.
"We're just trying to be original and funny by catering for all different types of humour, we don't set out to deliberately upset anyone."
James Mildred, communication manager of Christian Action Research and Education (CARE) said this is something that is deemed "deeply" offensive to many Christians.
According to the Independent, he said: "It highlights a fundamental hypocrisy that Christianity is seen as fair game to mock, disparage and insult.
"As Christians we believe it is vital to exercise respect when sharing our views and listening to what others think. This card is the opposite of respectful.
"Sadly, this happens every Christmas, which is such an important time in the Christian calendar. It is just another sad example of the kind of under the radar discrimination Christians around Europe and currently facing."
Dennis added if the cards do not fit people's taste, they have plenty of other options.
"If they want a more traditional Christmas card or something more mainstream then they shouldn't be looking at our range," she said.
"There's plenty of choices available out there for those who believe Christmas and comedy don't mix."
Listen to James Mildred speaking with Ruth Sax on Premier News Hour here:
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