Are millennials now embracing the American Dream?

Millennials don't buy houses. They are urban, mobile, risk-averse and saddled with student debt. Homeownership is about as enticing to them as a phone with a cord. Millennials are considered "generation rent."

"Young people today seem to have a less warm attitude toward housing. I don't know why, I'm not one of them," said Robert Shiller, Nobel laureate and co-creator of one of the most widely watched home price indexes.

But do they really hate homeownership? Sure, they lived through a recession and saw what it did to their parents' finances. And, sure, millennials came out of the recession with the highest unemployment rate of any age group. But, still, do they really hate homeownership?

Meet Ashley and Ken Wetzel. Married-with a condo.

"I wouldn't say that the entire generation is just anti-homeownership," said 28-year-old Ashley, who works in finance.

"We started working right out of college, we had good jobs right out of college, so we were able to save money over the years," said Ken, an engineer and also 28 years old.

The Wetzels were renters for six years. They married in the spring of 2013 and continued to live together in Washington, D.C. as renters-until the math just didn't add up anymore. The rent was getting more expensive than a potential purchase, and then there were other domestic downsides.

"There were things we wanted to change in the apartment, and we couldn't make them because we were renters. We needed approvals and things like that," Ken said.

"We figured it was time," Ashley added.

So they bought a two-bedroom condominium, using a 30-year fixed mortgage, in a quaint townhouse in the heart of D.C.'s Dupont Circle. The extra bedroom is an office now, but they hope it will become their baby's room someday.

Read More Selling my daughter on homeownership

Today there are just 13.3 million [U.S.] households, both rental and owned, headed by millennials, but this number will nearly double in the next five years, according to a new report from the Demand Institute. Researchers there looked at people ages 18-29, although the generation is more commonly seen as ages 18-34, a group consisting of 73 million people, per the U.S. Census. Millennials are expected to spend $1.6 trillion on home purchases over the next five years. In fact, 74 percent of millennials surveyed by the institute last summer said they expect to move in the next five years and nearly half of those said they expect to buy, not rent.

"Based on stated aspirations, there is no indication that this generation will be any less likely than previous generations to own their own homes," wrote the survey's authors.

Read More Millennials start leaving Mom and Dad's nest

So why are millennial homeownership rates still falling today? Why are first-time home buyers still not returning to the housing market in their historical numbers? A lot has to do with lifestyle changes and credit availability. Millennials get married and have children later in life; these are the two biggest drivers of homeownership. While their employment is improving, it is not improving as fast as other age sets, and some have had trouble building the credit scores necessary today for obtaining a mortgage.

Rising rents have also kept some urban millennials from saving for a down payment on a home, but affordability in general is actually improving for young adults, at least according to an analysis by Fannie Mae:

In 2013, fewer than one in four young homeowners paid more than 30 percent of household pre-tax income for monthly housing costs, a rate of affordability problems that is 13 percentage points lower than in 2007 and more than 2 percentage points lower than in 2000, prior to the mortgage credit bubble.

While the homeownership rate for millennials is still falling, by 0.4 percentage points between 2012 and 2013, this was the first time since 2008 that the homeownership rate for young adults did not fall at a faster pace than the rate for all households, according to Fannie Mae. It was also was the smallest annual drop measured for this group since the beginning of the recession.

The tides may slowly be turning, but that does not mean this generation will be the same type of home buyers their parents were. First of all, they are a lot more savvy about the financing, given what they saw in the recession and given that they will, in general, buy later in life.

"I think we just have a little bit more life experience. My parents got married younger, they bought younger," Ashley said.

"I didn't want to be another statistic or another number of someone who got in over their head because they didn't understand what they were getting into. I didn't want to live and work just to support my four walls," Ken added.

Watch: Why millennials remain key to the housing market

And one stereotype that rings true, at least for the Wetzels, is they have no desire to move out to an oversized house in the suburbs, an expectation that the nation's home builders have been banking on.

"That's definitely not the plan. We plan to stay in the city for as long as we possibly can," Ken said.

"I think there is a lot to be said for staying in the city your whole life and when and if you have kids, raising them here," Ashley agreed.