"It's a terribly exciting time for them," a family friend tells PEOPLE

By Simon Perry and Michelle Tauber
Updated May 06, 2015 08:00 AM
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In their first days as parents of two, Prince William and Princess Kate have been quietly bonding with their children at home like any other family welcoming a new baby – except home is a palace and a visit from great-granny means a pop-in by the Queen herself.

Since arriving home on May 2 just hours after Princess Charlotte’s birth, the new family of four “have been enjoying nice, private family time,” a close palace source tells PEOPLE in this week’s cover story.

With a boy and a girl – not to mention an heir and a spare – to dote on, William, 32, and Kate, 33, are relishing the early days of their growing family.

“It’s a terribly exciting time for them,” says a family friend.

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As they prepare to set up their home base at their country estate, Anmer Hall – some three hours northeast of London – Kate is enjoying her time off from royal duties and William is readying to return to his nearby job as an air ambulance pilot.

“They are very settled, his job is set, they have their house, and the status quo hasn’t changed in the royal family at large,” says the family friend. “So they are looking forward to a period of calm.”

For much more on Princess Charlotte’s first days at home with William, Kate and big brother George, pick up this week’s issue of PEOPLE, on newsstands Friday