Stanton and her fiance, who got engaged on Bachelor in Paradise this past summer, gave an update on the status of their relationship during an appearance at 102.7 KIIS-FM's Jingle Ball on Friday.
"We're enjoying life, enjoying the kids and having a good time," Murray toldEntertainment Tonight. "We love each other. We're having a blast."
Stanton has two little girls, Charlie and Kinsley, from a previous marriage.
"I feel like we've been through a lot in the past couple of months," Stanton disclosed. "I mean, kind of merging our families together. He brought his dog with him, he's meeting my kids. So, it's been a lot, but I feel like we've definitely gotten stronger through it. We're really happy."
"He moved across the country to live with us," Stanton said, referencing how Murray moved from Atlanta, GA, to Orange County, CA, after the show. "And it's been different, but it's been good. We like it."
When asked whether he made the right choice to uproot his life for Stanton, Murray replied, "It's been a great decision. I love her little ones more than anything, so we're having a lot of fun out here and we're excited."
The couple was also scrutinized during and after their time on Bachelor in Paradise. Murray's intentions were frequently questioned, and Stanton was criticized for dumping new The Bachelor star Nick Viall in favor of her polarizing fiance.
"I tried to stay away from social media and what everybody says, but I know it's tough because she wasn't used to the criticism and neither was I," Murray said.
"The way everything was portrayed, it made [our relationship] seem like it was bad -- so we understand people's concerns, but there's no concern for us. Hopefully people see how we are in real life, and we're having a great time."
The engaged couple has yet to set a wedding date but insist fans shouldn't read into it.
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"We've talked about it a little bit, but we've been so busy and hectic in our own lives," Murray revealed.
"Hopefully planning a date soon, right?" Stanton asked Murray.
"Yeah, absolutely," the former pro baseball player confirmed.
As for their immediate holiday plans, Stanton and Murray will be merging their families together for Christmas.
"His family and my family are all flying out to Orange County, so we're going to have like, a big family get-together, which will be fun," Stanton said, adding that she's never had a real Christmas tree and buying one with Murray is on her to-do list.
"It's going to be a lot of fun," Murray elaborated.
"[It's] my family's first time kind of traveling for the holidays to the west coast. They love Amanda and the kids. The first time they met them was in Kansas City; we brought them up to see one of my brother's games and they fell in love immediately. So, they're excited to see them."
Murray also admitted he wishes "nothing but the best" for Viall with The Bachelor's Season 21 premiere right around the corner on January 2.
"We've moved on from everything," Murray said of his former The Bachelorette rival. "We're very happy in our lives, and we wish him nothing but success in his."