Prince Albert, Princess Charlene of Monaco open up about their marriage

Royals: Prince Albert and Princess Charlene
Prince Albert and Princess Charlene speak to CBS News about their recent marriage.

(CBS News) The Prince and Princess of Monaco celebrated their first anniversary this month and recently discussed their marriage in a rare interview with CBS News.

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Though the couple is perhaps less well known than Prince William and Kate, Duchess of Cambridge, their wedding was a celebrated event, just weeks after the British royal wedding last summer.

About 800 miles due south from London, Prince Albert of Monaco married Charlene Wittstock - a former Olympic swimmer from South Africa. It was a glittering ceremony, studded with celebrity guests.

A year later, the couple invited "CBS This Morning" into their home - the 700-year-old princely palace, perched on a clifftop above the emerald waters of the Mediterranean.

Pictures: Prince Albert
Pictures: Princess Charlene

"Well, I think it's, wonderful," Prince Albert said about married life. "I can't speak for Charlene, but she will be able to answer you. But we're having a wonderful time."

"Great. I recommend it," Princess Charlene said.

Prince Albert's family has ruled Monaco since the 13th century. The tiny country is less than one square mile in area, but what it lacks in size it makes up for with its wealth. Monaco is famous as a playground of the super-rich. As residents they pay zero income tax, and they're not shy about showing off their money. It's a big change for the former athlete whose father was a photocopier salesman.

So how is life being a princess? Princess Charlene said, "Yeah, it's great. It's I don't know how to answer that, honestly. What's it like being a princess?"

At that point the prince asked for the interview to be paused. It's clear that his wife is still finding her way in a very different world from the one she grew up in.

The last princess of Monaco - Prince Albert's mother - was Grace Kelly. She brought Hollywood glamour to Monaco in the 1950s when she married Prince Rainier. The press called it the wedding of the century.

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Asked about the similarities between Princess Grace and Princess Charlene - and if he noticed similarities with his wife when they first met - Prince Albert said, "Now I think you know every human being is unique. And that's the beauty of the human race. I knew that whoever I choose to marry, that she would be compared to my mother. And I was ready for that. But I think Charlene has her own very wonderful personal qualities to be able to shine."

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When asked what qualities drew him to Princess Charlene, a palace official decided that question was too personal, perhaps understandably given that the couple's private life is the source of constant tabloid speculation.

At 54, Prince Albert is 20 years older than his wife. Dubbed a playboy prince by the media, he fathered two children out of wedlock. When he finally decided to settle down, many in Monaco heaved a sigh of relief. But the wedding was marred by rumors that the bride was having second thoughts.

Just days before the wedding, French newspapers reported that the bride had tried to run away and fly home to South Africa. Then, during their honeymoon, there were stories that the prince and princess were staying at separate hotels.

"I mean, to be honest with you, I really do not read anything that's printed," Princess Charlene said. "I think rumors, the word is, says a lot about itself, I suppose."

"Those rumors were completely unfounded, completely untrue," Prince Albert said. "And it was very unfair to, the - and we know the source. But, and we've been able to deal with that. But it was a very unfair treatment."

Princess Charlene retired from competitive swimming five years ago. But now she's returned to the pool-side to host the South African swim team as they prepare for the London Olympics. "Well, you know opportunity presented itself to the team I just thought, you know, I would like to extend an offer to the South African team to come and acclimatize here before London."

Chad Le Clos will be competing against Michael Phelps in London. "Back home I think nearly every single person that I see on the street will come up and ask me, 'Have you met the princess?' and I'm like, 'Yeah, we were in Monaco'. We've seen her a couple of times. It's awesome."

The princess said she sometimes misses competing and that she loved the discipline of training. Long before she met Prince Albert, swimming was her world. Now the determination that made her a champion in the pool is helping her adapt to her new job as a princess.

"I'm still in the process. You know, it's a process. Everything is a process," Princess Charlene said. "And I think I've got a bit of time on my side."

For more from this interview with Prince Albert and Princess Charlene, watch the video in the player above.