Irish passport

It basically means he can travel with EU citizens rights, if he travels together with you, but not if he travels alone. You should carry proof of your marriage. 

https://www.spanishpropertyinsight.com/2021/04/14/brits-married-to-eu-citizens/

Thank you for that information, do you know if his passport will still have to be stamped at the airport?

I read somewhere on an official link that it shouldn't be stamped. Unfortunately I can't find the link. I'm UK citizen with a Danish resident card and there is never any passport control when I arrive. 

Yes, his passport will be stamped but it won't matter as long as he his travelling with you.

This link is from an Offical EU websites and therefore more reliable:

https://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm

And legally, you both can only stop within the 90 day rule before registering with the authorities. 

Steve 

On the strength of tebo53's response this is the offical wording from the Department of Foreign Affairs in Ireland for all Irish citizens:

Staying for longer than three months

All EU citizens who want to stay in Spain for more than three months have to register in person at the Oficina de Extranjeros (Foreigners Office). You will be issued a Certificate of Registration with your name, address, nationality, identity number (NIE) and date of registration. The certificate serves as confirmation that you have registered, but is not recognised by the local authorities as a valid form of identification.

You can find further information by clicking on this link:

https://www.dfa.ie/travel/travel-advice/a-z-list-of-countries/spain/#:~:text=For%20Irish%20citizens%2C%20acceptable%20forms,in%20your%20wallet%20or%20purse.

I am in the same situation, every time I travel with my Irish wife. I have never been allowed to go in the same queue. I have always had my passport stamped and have asked immigration about the 90 day rule when I travel with my wife. It’s the same answer every time, you are a U.K. citizen and you can stay for 90 days. I hear lots of people talking about different rules when you travel with your EU spouse but I have challenged this dozens of times at Spanish immigration and get the same response every time. If anyone else has had a different answer I would be delighted to hear how. I understand EU citizens can only stay for 90 days also but they do not need to wait another 90 to return, this is the issue I am trying to overcome. 

Why not apply for a Visa for Family Members of a Citizen of the Union. Details in the following link:

https://www.exteriores.gob.es/Embajadas/kingston/en/ServiciosConsulares/Paginas/Consular/Visados-para-familiares-de-ciudadanos-de-la-Union.aspx#:~:text=Family%20members%20of%20citizens%20of,the%20way%20to%20joining%20them.