My husband has an Irish passport and I have a UK passport. We would like to travel together to Spain for 6 weeks in October/November, and to Tenerife for 2 x 5 weeks stays in December to March. As this is over the 90 days in 180, is this still allowed because my husband has an Irish passport?
Since you are traveling with your husband, this journey is covered by the EU freedom of movement. As long as each trip lasts less than three months you don't have to register or prove anything. You do not need a visa either. That's “three months”, not “90 days in any 180 day period”; the latter only applies to people who are not covered by the EU freedom of movement (including most British citizens, even yourself when you are not accompanying or joining your husband).
Just walk with your husband through the “EU/EEA passports” lane. Out of an abundance of caution, you may want to carry proof of your marriage (for example if the last name on your passports are different) but I doubt even that is necessary.
A stay longer than three months would also be easier for you as the spouse of an Irish citizen but, as a third country national, you would in principle have to get a residence card (your husband doesn't need one) and both of you might have to complete some other formalities (registration, proving you have health insurance).
If you do not leave Spain at all in your whole trip (that's Spain specifically, not the EU or Schengen area), the rules for a stay longer than three months would technically apply but the consequences of missing registration are minimal (a fine at most) and authorities are unlikely to bother you. If you are actually going to two or three different places then there is no reason at all that the question would even come up.