Of note, a higher percentage of respondents reported to be single parents but acknowledged co-parenting with someone else.

FORBES: The Happiest Working Mothers Don't Always "Have It All"

Results showed that couples had a stronger, more supportive co-parenting relationship when the father spent more time playing with their child.

FORBES: Dad's Off The Hook? Study Says Fathers Should Be A Little Less Involved In Parenting

Family by Design matches people who aren't in a position to have a child on their own with others to share co-parenting responsibilities.

WSJ: Tech's Over-Sharing Economy

"Ms. Grigorieva will now concentrate on co-parenting Lucia, resuming her charitable work for the children of Chernobyl and moving forward with her life, " the statement said.

CNN: STORY HIGHLIGHTS

But when the father participated more in caregiving, like preparing meals for the child or giving baths, the couples were more likely to display less supportive and more undermining co-parenting behavior toward each other.

FORBES: Dad's Off The Hook? Study Says Fathers Should Be A Little Less Involved In Parenting

Kyle Pruett, a leading child-development researcher and co-author of a 2009 book, "Partnership Parenting, " says Mr. Grossbauer's and Ms. O'Callaghan's differences, typical for many couples, can benefit the children.

WSJ: At-Home Dads Make Parenting More of a 'Guy' Thing