It seems from online research (links below) that a "pareja de hecho" is a registered live-in relationship and would not necessarily count as a marriage or a civil partnership.
http://www.velascolawyers.com/en/civil- ... hecho.html
http://www.tumbit.com/how-to-guides/art ... hecho.html
However, if you can prove a "durable relationship" with your partner, you will be considered an "extended family member" for the purposes of the EEA Regulations.
The UK interprets a durable relationship as having lived together for two years in "a relationship akin to marriage". Proofs required will be joint bills for the last two years, etc.
Can the mods also move this thread to the EEA Applications sub-forum?
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.