George Gilder discusses this in his book Men and Marriage but the data he uses is three decades old. There may be a way to get at the question via US Census data on households but the questions differ from survey to survey and tend to report household totals without breaking down individual income contributions.
Fortunately, there are a couple of GSS items perfectly suited for investigating the sex distribution in income among married couples. The GSS asks about both a respondent's individual income and the respondent's household income. Both figures are inflation-adjusted.
In contemporary married American households, men account for 64.7% and women for 35.3% of family income by median average and a virtually identical 64.1% and 35.9%, respectively, by mean average.
A few technical notes:
To avoid racial confounding, only whites are considered.
For contemporary relevance, all responses are from 2008 onward.
The age range considered is 30-65. Mean and median household incomes are very similar for men and women. We're looking at a random sample of male and female spouses however, not a sample of married couples with data for each spouse in each particular marriage. Men show up a couple thousand dollars higher in aggregate here, presumably because men tend to be a little older than their wives and income increases with age into a person's sixties.
Men's and women's individual reported incomes both come to modestly more than family income, presumably on account of investments, dividends, savings accounts, etc being counted both individually and when reporting the entire family's income.
For example, the husband makes $50k, the wife makes $25k, and together they have $5k in investment income. This leads to the husband reporting his annual individual income as $55k and the wife reporting hers makes $30k. The total household income will be reported by both of them as $80k, but if each of their individual incomes are summed without regard to reported total household income it will appear as if that total household income is $85k rather than $80k. This is easy to adjust for and is adjusted for in the reported results.
The male and female sample sizes using the parameters listed above are 867 for men and 791 for women, so the law of large numbers kicks in. Extending back to the year 2000 increases the total sample size to 4,478 and the median average and mean average splits are 65.4%-34.6% and 64.6%-35.4%, respectively.
In other words, the data is good. Among married couples in the US (at least among whites), men earn on avearge a hair under two-thirds of the family's income and women a hair over one-third of it. That's basically the way we think it should be.
GSS variables used: SEX, YEAR(2008-2014), CONINC, CONRINC, AGE(30-65), RACECEN1(1), MARITAL(1)