Thomas Sowell makes a similar point about stagnation of "household" income. The demographics of households have changed dramatically, with a large increase in households with single adults, and single non dependent adults. Two incomes make less money than one, so household incomes can look worse.
I don't think this accurately captures any real issues with young dependent adults, but that's just another instance of the problem of summary statistics of heterogeneous aggregates.
Ah, yeah, I looked up the median household income and was slightly surprised it hadn't dramatically increased as you'd naively expect if the OP's explanation is right. Thanks for explaining :)
ETA: The table linked by Landsburg has been called into serious question by Evan Soltas [H.T. CronoDAS]. I edited the post to leave only the table to provide context for the comment discussion of its status.
Economist Steve Landsburg has a post [H.T. David Henderson] about the supposed stagnation of median wages in the United States in recent decades. In the linked table median wages have risen for: