"I couldn't be more in love with my family," NPH, 41, posted to Instagram, captioning a photo of David, 39, with their two children. "Any reports to the contrary are woefully mistaken. #grateful"
Neil and David became the parents of fraternal twins -- Harper and Gideon -- via a surrogate in October 2010.
The couple has been engaged for years and plans to marry, although no official wedding date has been set.
Neil announced the engagement in 2011 after New York legalized same-sex marriage, Tweeting, "David and I did propose to each other, but over five years ago! We've been wearing engagement rings for ages, waiting for an available date."