What are the female and gender-neutral equivalents of ‘henpecked husband’

Cock-pecked is the traditional counterpart, as the cock (or rooster) is the male counterpart to the hen.

The Oxford English Dictionary puts its first use in 1753:

1753 An Essay on Celibacy 96 Male usurpation, or being cock-pecked, depends for the most part on the want of good nature, and a little submission in the female.

The 1912 Dictionary of Slang and Colloquial English puts it thus:

Cockpecked. Masculine home-rule: spec. of a tyrannical kind: cf. Hen-pecked.

It is uncommon today, thank God, but it comes up occasionally in song lyrics and other places. Here's Yoko Ono:

So don't try to make cock-pecked people out of us

In addition to the accepted answer, I frequently see the word cowed wife to describe these women even back to the Victorian Era.

To cow someone is to destroy their resolve or courage, typically through violence or intimidation. Intimidation can also be the same type of verbal abuse that henpecked husbands receive.

Henpecked husbands tend to be cowed by their wives, too. So, apart from the alliterative appeal of henpecked husband, they could also be cowed husbands.