Barrington attributed the rise in fees to regulations stemming from the financial crisis. As a result, he said, some of the money-making opportunities that financial institutions have depended on have been cut off. Banks have been forced to take a much sharper look at their fee policies, including free checking, he said.

A significantly higher number of credit unions either provided free checking or a path toward free checking.

Claes Bell, a banking analyst at Bankrate, said the percentage of credit unions providing free checking rose to 76% in 2015 from 72% the year prior.  

"Even as free checking has declined at banks, this year we saw an increase in free checking at credit unions," Bell said. "It shows that credit unions use that as a way of differentiating themselves from banks. There's nothing more people hate than bank fees when it comes to financial services."

Credit unions differentiated themselves further by providing a path to free checking. The average minimum balance required to waive checking account maintenance fees at credit unions ranged from $500 to $2,500, according to Bell.

Banks, however, reported a higher average minimum of $6,847.49 – an increase of $800 over the last six months, according to MoneyRates.com. The balance requirement jumped from $3,590.83 in four years.

Credit unions also beat out banks in ATM fees. The average out-of-network ATM fee charged by banks increased to $1.73, up 12 cents in the past six months, according to MoneyRates.com. Non-customers were charged an average of $2.87 per transaction at banks.

Bankrate reported credit union members were charged an average of $1.50 per transaction for out-of-network ATMs. What was noteworthy, however, was that a credit union member may not be charged an out-of-network fee for all transactions. Nearly one third of credit unions surveyed do not charge their members out-of-network ATM fees, or allow for at least one fee-free transaction per month.

"The thing with fees is like squeezing one end of the balloon, you put the squeeze on one type of fee and the bank is going to look for ways to make it up," Barrington said.

With the number of physical branches on the decline, banks see the use of expensive ATM networks as a prime way to make up for lost fees, he added.

Banks also fell short compared to credit unions when it comes to overdraft fees. According to Bankrate, credit unions charged a slightly higher fee at $26.96, up from $26.78 last year. Banks, however, averaged $33.07 per overdraft in 2015.  

However, as the CFPB is preparing a rule on overdraft fees and called for financial institutions to offer no-overdraft fee accounts, the fee landscape may change over the next couple of years, according to Bell.

A model that allows for free checking may not be viable if there is a crackdown on overdraft fees, he added.

"As much as people don't like paying maintenance fees, you would be hard pressed to make it work without overdraft or maintenance fees," Bell said. "I don't know where they will make up that shortfall if there is a crackdown on overdraft fees."

Consumers can control most fees they are charged, such as overdrafts, for the most part by practicing good banking habits and avoiding the use of out-of-network ATMs, according to Barrington.

"But monthly maintenance fees are going to be there month in and month out, no matter how good your banking habits are," he added.

The only thing a consumer can do to avoid that fee is change their financial institution to one that does not charge it or offers a lower fee, Barrington said.