Are they eating HOT DOGS? Gwyneth Paltrow and Chris Martin treat their kids to food truck fare on rare public family outing

PUBLISHED: 11:50 EST, 12 March 2014 | UPDATED: 17:15 EST, 12 March 2014

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In their 10 years of marriage, Gwyneth Paltrow and Chris Martin have made it their mission to stay mostly under the radar.

They avoid walking red carpets together and it's a rare occurrence indeed to see them pictured together with their two young children.

But on March 7, they gave fans a glimpse into their private world as they enjoyed a decidedly low-key outing in Venice Beach, California.

Rare family sighting: Gwyneth Paltrow and Chris Martin enjoyed a fun night out with their children Apple, nine, and Moses, seven, in Venice Beach, California on March 7, where they took in the monthly First Fridays event on Abbot Kinney Boulevard

The foursome headed out on foot to take in the monthly extravaganza known as First Fridays on Abbot Kinney Boulevard, which sees every kind of food truck imaginable line the jam-packed street.

While the family are known for their strict diet, with the 41-year-old actress a long-time devotee of the macrobiotic diet while her Coldplay frontman husband is a vegetarian, they clearly decided they deserved a night off, as they were spotted enjoying a fast-food meal from the Dogtown Dogs truck.

Serving just a limited selection of hot dogs and tater tots, it's a processed food-phobic's nightmare.

Not that the Iron Man star seemed to mind in the slightest, appearing in good spirits as she enjoyed her family outing with her brood.

One stylish mama! The 41-year-old looked effortlessly chic as always in black pants, matching flats, a white top featuring an unusual ruffled design and a striking black and white patterned cropped leather jacket

The Oscar-winner looked like any other trendy mother as she sauntered down the street dressed stylishly in black pants, matching flats, a white top with unusual ruffled design and a funky black and white patterned cropped leather jacket.

She wore her long blonde locks in her signature poker-straight style, while she appeared to be make-up-free, shielding her eyes behind large black sunglasses.

Her 37-year-old husband was clad in his trademark casual all black outfit, consisting of jeans, a T-shirt, jacket and high-top sneakers.

Leader of the pack: The Oscar-winner led the way through the crowd on the busy street as her gorgeous family followed closely behind, with Coldplay frontman Chris bringing up the rear, slipping on a black baseball cap as he attempted to go unnoticed

Natural beauty: The Californian-born star wore her long golden tresses in her signature poker-straight style, while she shielded her make-up-free face behind large black sunglasses

The couple's gorgeous children - Apple, nine, and Moses, seven - were equally casual for the outing.

Apple looked sporty in navy blue leggings, a matching tee, bright blue sweatshirt and knee-high brown Uggs, while he brother opted for a similar style, in black jeans, black and white checked canvas shoes, a green t-shirt and white hoodie.

On Tuesday, Chris and his band, Coldplay, kicked off the iTunes Festival at SXSW in Austin, Texas.

The British rockers debuted four new songs from their highly-anticipated upcoming album Ghost Stories, which drops on May 19.

That's not on the macrobiotic diet! The notoriously strict, health-conscious parents treated their kids to a hot dog and tater tots from the Dogtown Dogs food truck