"Finally on our third single, it feels like we have everyone in our corner and things are finally taking off," Hannah Mulholland tells PEOPLE

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Earlier this month, Runaway June made history.

The country trio made up of Naomi Cooke, Hannah Mulholland and Jennifer Wayne broke into the top five on the Mediabase Country Chart with their hit single “Buy My Own Drinks,” marking the first time a female trio has accomplished that feat since 2003.

The last female trio to do it was the almighty Dixie Chicks.

“To even be mentioned in the same sentence as the Dixie Chicks is pretty heavy,” Runaway June’s Naomi Cooke says during a recent interview with PEOPLE. “We were really absorbing music and becoming artists at the time when the Chicks were on top of the world. I think all of us have really been inspired a lot by their music. I think that’s unavoidable. But the comparisons? Well, we are very different.”

Indeed, while making comparisons between the past and present musical trailblazers of country music might be fairly easy to do, it isn’t necessarily fair.

“The Chicks were like Natalie and the sisters,” recalls Cooke, who handles lead vocals and guitar for the band. “With us, we are very individual and we have individual styles and we have individual hobbies … even sonically we sound different. But we love the Chicks. They are like an untouchable thing.”

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Hannah Mulholland, Naomi Cooke and Jennifer Wayne of Runaway June
| Credit: Ben Trivett

And while the Chicks’ place in the country music history books might be in fact untouchable as far as all-female trios go, it doesn’t mean Runaway June won’t try to reach those heights. They’ve been fighting their way towards the top since first coming together as a group back in 2015.

“It has been a long journey for us,” admits Hannah Mulholland as she prepped for a recent performance in Chicago. “Even the journey before getting our record deal was a long one. You have to really put in the time. You need all hands on deck for a song to work. So finally on our third single, it feels like we have everyone in our corner and things are finally taking off. It feels more exciting than if you just came out and you were just this big whirlwind right off the bat. We know how much goes into making sure your song is played on the radio.”

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Naomi Cooke, Hannah Mulholland and Jennifer Wayne of Runaway June
| Credit: Kristin Barlowe

Obviously, the plight for female artists to get their songs played on country radio is one that Runaway June and countless other female artists have endured together over the last decade. But currently, their hard-fought struggles seem to be finally turning the corner.

It also helps to have Carrie Underwood in that crucial corner with you.

“I think the second she invited us to go on tour with her, everyone was like, ‘Oh wow, she’s giving you the stamp of approval — I will take a look at you,’” recalls Jennifer Wayne regarding their place on Underwood’s Cry Pretty 360 Tour alongside fellow openers Maddie & Tae. “She’s really given us the platform to play for so many people every single night. I definitely think that that is a big part of why we are here.”

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Hannah Mulholland, Naomi Cooke and Jennifer Wayne of Runaway June
| Credit: Kristin Barlowe

Underwood has taught Runaway June much about life offstage, too.

“Carrie has never been handed a damn thing,” says Cooke, who will join her Runaway June bandmates on Good Morning America on Oct. 3. “She has an incredible work ethic and she is an extremely smart businesswoman. For us to be able to see her out there with her husband [Mike Fisher] and children [sons Isaiah, 4, and Jacob, 8 months] gives us hope because we all want families and we don’t want to give up our careers.”

She adds, “This is a very difficult job to do, so being able to see her and Mike do it the way they do shows us that it can be done. We don’t have to have one or another. We can have it all.”

And currently, Runaway June is getting that much closer to having it all.

As “Buy Your Own Drinks” remains cozy in the top five, the trio has released their long-awaited debut album Blue Roses and has already announced their next single “Head Over Heels.”

But for the women of Runaway June, they refuse to take anything for granted.

“It’s really a rough industry,” says Mulholland, who alongside with her bandmates previously flirted with the Top 40 via songs such as “Wild West” and “Lipstick.”

“I feel like you are never really safe in the music business. You always have to be pushing to work really hard and to show up on time and play good music. You can never just take a breath and say you ‘made it.’ We spent four or five years pounding the pavement. There were a lot of early mornings where we thought we weren’t getting anywhere … and then you look back and you realize that we had to do every single one of those things to get where we are right now.”