In her Christmas message, the Prime Minister also paid tribute to the "heroes" in the emergency services who responded to the Grenfell Tower fire and "abhorrent" terror attacks in Manchester and London.
Unlike last year, Mrs May makes no mention of Brexit, but calls on Britons to "come together confident and united" at Christmas.
In contrast with Jeremy Corbyn's Christmas message, which makes no mention of religion but emphasises a message of "compassion", Mrs May, who grew up in a vicarage, repeatedly refers to Christianity and its values.
The Labour leader has previously refused to discuss whether he holds any religious beliefs.
In her Christmas message, the PM said: "As we gather with our friends and family, I want to say thank you to all those whose service to others means they will be spending time away from their loved ones this Christmas.
"Men and women in our armed forces, whose humbling bravery and daily sacrifices help to ensure the security of our nation and our allies around the world.
"The heroes in our emergency services, whose courage and dedication so inspired the nation in response to tragedy at Grenfell Tower and the abhorrent terrorist attacks in Manchester and London. But whose service saves lives in our communities every day, including Christmas Day.
"And the thousands of volunteers in our country who will give up their time to make someone else's Christmas that little bit better: from faith inspired projects like the Churches Together initiative in my own constituency - to aid workers helping those in war-torn parts of the world.
"As we celebrate the birth of Christ, let us celebrate all those selfless acts - and countless others - that epitomise the values we share: Christian values of love, service and compassion that are lived out every day in our country by people all faiths and none.
"Let us take pride in our Christian heritage and the confidence it gives us to ensure that in Britain you can practice your faith free from question or fear.
"Let us remember those around the world today who have been denied those freedoms - from Christians in some parts of the Middle East to the sickening persecution of the Rohingya Muslims.
"And let us reaffirm our determination to stand up for the freedom of people of all religions to speak about and practice their beliefs in peace and safety.
"So this Christmas, whatever our faith, let us come together confident and united in the values we share. And wherever you are at this special time of year, let me wish you all a very happy Christmas."
The Prime Minister regularly attends a church in her constituency of Maidenhead, Berkshire.