That is very weird..The text of the original question has disappeared! I wanted to revisit this question because I made a mistake in my answer. See my new answer below.
CORRECTION: I was incorrect in my original answer (below). The highly skilled worker visa is an exception. You CAN in fact get a work permit as the spouse of a highly skilled worker. I spoke to Sterna Abogados about this. You might want to consult with a lawyer to find out exactly the steps to obtain your work permit. Perhaps your husband’s company would allow you to consult with their lawyers.
This was my originally incorrect answer: Hi there! You typically don’t automatically get a work permit if you come to Spain as a spouse. However, if you have a college degree and can be considered “highly skilled”, you can apply for a work permit under the highly skilled scheme after you arrive to Spain. You need a formal offer from a company to qualify for this, but once you are already in Spain and are able to do some in-person networking, it’s much easier to do! If you went to a “prestigous university”, you can get apply with any type of job offer, it doesn’t have to be in any specific sector or at a large company.