Short answer: no, he does not have the same rights as a European citizen. His right to stay is a consequence of your right of free movement.

However, things are improving slowly, and in theory he should be able to travel in Europe with only his passport and the residence card. In practice that only seems to work between Schengen countries. So if you are in the UK, getting into Spain might be difficult. I can't imagine that they would refuse your husband if you travel together, but you better check with the Spanish embassy.