Nick Lachey and Vanessa Minnillo Adopt a Husky

Happily back together after a brief split last year, Nick Lachey and Vanessa Minnillo have taken a big step in their relationship: Adopting a dog together! At a party in Los Angeles honoring the new documentary Hungry in America Sunday night, Lachey told PEOPLE that he and his girlfriend adopted the pup earlier that day. "Now that I say it on record I'm going to have to keep him," he joked.

The 1-year-old Siberian husky, named Kona, was on display at a roadside adoption event in Los Angeles. "I was driving down Ventura and we saw rescue dogs on the side of the road," he explained. "Vanessa was with me — I don't make those kind of decisions alone anymore — but since I grew up with a husky, I couldn't resist."

Calling huskies "independent" and "stubborn by nature," Lachey said they're harder dogs to train "because they can be aloof. They need a lot of exercise, but once you let them know that you're the alpha male, they're very loyal, great dogs." The American Kennel Club calls the breed friendly, alert and intelligent, making the dogs "agreeable companions" for any family.

So now that the couple has this new pet, who's going to be the stricter parent? "It's too early to tell," laughed Lachey.

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Kate Hogan with reporting by Shayna Arnold