by her running the "show" somehow i doubt he means he's the one playing housewife.
they both work, they both make shitloads of money and they're both powerful people. in a sense, in terms of power, they're equal. they're in as good a position as you can be in for defying the stereotypical male vs female role in relationships.
plus, his "constant flow of dialogue" quote suggests they're approaching it in a healthy, democratic way. probably the best way, given you can avoid coercing one side into a role they don't want to be in.
ppl always feel the need to arbitrarily place a hierarchical structure over every relation. then you get them to fess up on their rationale and they prove they don't know what the fuck they're talking about.