The Spanish word pareja means two different things and yes, one of them is couple.

But couple refers to two things seen as ONE UNIT.

I went out with a couple (un par) of friends.

Leo has a couple of dogs. 

If you’re talking about the one person you share your life with, that is the other meaning of pareja, your partner.

I went out with my partner. (NOT I went out with my couple.)

She has a partner. (NOT She has a couple. A couple of what?)

I hope that’s clear!