In this situation, you are indeed entitled to residence card as family member of an EU citizen, which should generally be easier to obtain than a residence permit. It's definitely the case if you are married or in some form of registered civil partnership, possibly also if you can simply prove that you have a long-term relationship.

For more details you can look at previous questions covering these aspects of EU law with respect to other countries (but the rules are supposed to be the same everywhere), e.g. http://expatriates.stackexchange.com/questions/2441/can-a-non-eu-citizen-with-a-eu-partner-live-and-work-in-the-eu?rq=1, http://expatriates.stackexchange.com/questions/5645/moving-to-frankfurt-with-my-swedish-wife-i-am-not-eu-citizen, http://expatriates.stackexchange.com/questions/2500/what-is-the-process-of-getting-a-uk-visa-and-a-work-permit-for-a-non-eu-citizen?lq=1 or http://expatriates.stackexchange.com/questions/6056/us-citizen-with-eu-spouse-who-doesnt-yet-have-a-job?lq=1.

Regarding Spain specifically, [here is a brief summary in English](http://europa.eu/youreurope/citizens/residence/documents-formalities/non-eu-family-members-residence-card/spain/index_en.htm) on the EU Commission's website and [all the details in Spanish](http://extranjeros.empleo.gob.es/es/InformacionInteres/InformacionProcedimientos/CiudadanosComunitarios/hoja103/index.html) on the website of the Ministry of Employment and Social Security.