• Roughly 3 in 5 unmarried millennial and Gen Z couples live together, according to a new report.
• Half those couples don't split the mortgage or rent equally, and 37% feel like their relationship is financially unequal.
• "You're not going to have an answer that's going to be the same for each couple about what is fair," said a social psychologist.

Many Gen Z and millennial couples are moving in together before tying the knot to save money, but that doesn't often mean a 50-50 split when it comes to expenses.

Roughly 3 in 5 unmarried couples in the U.S. live with their partners, according to a report by the Thriving Center of Psychology, which surveyed 906 unmarried Gen Z and millennial pairs in June.

Millennial couples are more likely to live together, with 65%, versus 37% of Gen Z couples.

More than half of couples, 54%, said finances were part of their decision to move in together. But that doesn't mean they are splitting expenses right down the middle. Half of couples don't split the mortgage or rent equally, and 39% do not split pet costs equally, the survey found.

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What is possibly more concerning is 37% feel like their relationship is financially unequal.

Experts say the survey results underscore that when it comes to sharing expenses, equal isn't always equitable, or fair. However, the definition of fairness is likely to vary by couple.

"You're not going to have an answer that's going to be the same for each couple about what is fair," said social psychologist Michael Kraus, an associate professor of organizational behavior at Yale University.

'Seriously consider' splitting bills by income

"I advise young couples to seriously consider splitting the household bills according to income and then revisiting it every year as incomes change," said certified financial planner Cathy Curtis, founder and CEO of Curtis Financial Planning in Oakland, California.

For example, if your salary represents one-third of your household income, you might be responsible for a third of the rent. Couples should list all the household expenses, including fixed costs and an average for the variable costs, then split those costs according to income and deposit their allotted amounts monthly in a joint account, said Curtis.

This method can allow both people to have money left over after key expenses for goals such as retirement, especially the person with the lower income, she added.

"When I bring it up, I see relief in the face of the person making less money," said Curtis, who is also a member of the CNBC Financial Advisor Council. "I think it's totally fair [and] I think it makes for greater equity, less resentment and also creates more communication around money," she said. 

'It's almost not fair to split finances 50-50'

People come into partnerships from different financial situations, and that affects how they divide household expenses, said certified financial planner Sophia Bera Daigle, who is also the founder of virtual firm Gen Y Planning in Austin, Texas.

For example, one partner may be saddled with student loan or credit card debt while the other partner is not. The latter may have the financial strength to carry rental or mortgage expenses so the other person can focus on paying down their liabilities, said Daigle.

"I think it's almost not fair to split finances 50-50 without taking into account your partner's financial situation," said Daigle, who is also a member of the CNBC Financial Advisor Council. "It's really important to get a better financial picture of what's going on with your significant other."

Equity is 'about what roles you play'

Society and culture has shifted toward a place of more equality, allowing more women to make more money than they did 50 years ago, said psychotherapist Dr. Carli Blau, founder of Boutique Psychotherapy in New York. 

But a division still exists around financial responsibility and maintenance that depends on the role both partners play in the relationship, she said.

"It's no longer about financial equality; it's really about what roles you play in your partnership and do both people feel heard, seen, appreciated, supported and validated as a partnership," said Blau.

It's important for couples to have open and honest conversations about what their finances will look like once they move in together, because "part of becoming a couple is developing a way to live together that's neither yours nor theirs; it's what you create together," she said.

Your solution won't 'be a one-size-fits-all'

Fairness is going to be rooted in each party's perception of what is "fair," and those perceptions are often distorted and inconsistent with each other, said Kraus.

Couples that communicate and discuss how to manage the finances together and are transparent about their contributions are going to create the "splitting scheme" that they both consider fair, he said.

For instance, it might not be fair for one couple to split the mortgage or rent evenly because that would be "90% of my check and 40% of yours," said Kraus. "That might seem unfair to one couple but totally fair to another."

"It's not going to be a one-size-fits-all for each couple but it's really going to be based on this kind of communication," he added.

Couples risk dissatisfaction over perceived unfairness if they skip discussing their financial situations, cautioned Kraus. 

"If you're really serious about somebody and they're serious about you, being able to work through a discussion about fairness is something that you can definitely do."