When a check is made payable to a person and et ux such as in this example:
John Doe et ux
What is our endorsement liability when the branch did not have et ux endorse the check?

"et ux" definition is "and wife"

Latin isn't exactly known as a living language.

I am interested to see what people have to say about this, though.

While opinions will vary, I doubt anyone is going to cite you to any authority that is on point. Note this isn't the same as a check payable to "Bob Doe and Suzy Doe." Here, in addition to verifying Suzy's identity, you would need proof that "Suzy" is Bob's wife; i.e. proof of marriage.

Know that your bank guaranteed any "missing" endorsement that was required, but you will have to wait until you actually get sued on the missing endorsement to find out if a local court will say the drawer's direction was clear. Regardless, explain to the teller: "Ya gotta read these things before you hand them the money! If you don't understand the words pass the decision upwards or just say no."

Thank you for your response.
UCC endorsement rule lingers on.

Depending on your lawyer's sense of humor, one defense would be that under English common law the husband and the wife were one person and the person was the husband; e.g. she had no rights of her own or legal capacity of her own. Thus, anyone using the term "et ux" would be chargeable with knowing that if he signed that was all that was necessary.

I have to ask where the check came from or is this a hypothetical? Many questions are about "and" or "or" between two payees on a check or either being missing period. You've added Latin and that is quite unusual.

Checks that have "extra stuff" in the payee line are almost always the product of a system that always write checks based on how an asset in the names of the payees is held. For example, it's common to see a check for stock dividends payable in the form "John Jones & Sally Smith, JTWROS, TOD Sarah Jones-Smith" issued when stock is held jointly with a Transfer on Death beneficiary designation. Does that mean than Sarah Jones-Smith is a third payee? No. The only payees are John and Sally.

As for something payable to John Smith et ux, the genesis of the payee names may be property in which Smith's wife is a co-owner or has/had a dower right, and the property is recorded in the land records using the chauvinistic anachronism "et ux."