What procedures should we follow if my husband, who is on an O visa, needs to leave Thailand without me?

This post highlights the need for people to try to use correct terminology if they can.

We now know that the O/P is no longer on ANY visa :O and instead on a yearly extension of stay based on employment

AND

their spouse is not on a visa either but on a matching yearly extension based on being married to someone who legally works here.

This means IF they have a valid re-entry permit in their passports (which looks like the image Robert posted) they can indeed exit /re-enter thailand and will get stamped in until Oct 2019 when they return

Do the words re--entry permit sound familiar?

They don't tear out old pages of your passport. So it is clear now you are on an Extension of Stay vaild until October 2019. If your Re-Entry Permit has the word MULTIPLE under Number of Entries your are free to go and come back into Thailand and you will on every entry get the same date as the Extension of Stay is permitted up to ../../.. (october 2019)

Post a picture of the visa/ stamp in your passport then we will be able to advise

I posted a picture of the diference between a visa and an Extension of Stay, look in your passport and at that picture, which one is similar.

Perhaps you have an Extension of Stay - one year?

Check your passports again, you can NOT have a Non Immigrant B visa and do 90 day report, with the Visa you leave the country every 90 days.

This is an example of the re-entry permit:

A Multi-Entry can be a Multi-Reentry Permit...

Working visa does not exist. You applied for a multiple entry, does this mean you applied for the Extension of Stay at Immigration Office? Take a look at your passports to see the difference:

Where is here? Thai Immigration or at a Thai Embassy or Consulate?

Is he on a Visa, or is he on a waiting period? Without clear information we can only start guessing what you like to hear.

Because you are not even remotely clear I don't see how anyone can answer your question

What Visa are you in Thailand on?