Shouldn't a dark-skinned person's genes dominate those of a fair person?

I remember doing the gene pool stuff when I was in highschool and they said blue eyes are recessive and brown is dominant. My mum has green eyes brown hair, my dad has blue eyes blonde hair, I have green/blue eyes and blonde hair, so that makes sense. My fiance is dark skinned and has dark brown eyes and black hair and his parents are the same. When I had our daughter I didn't expect for her to look very much like me but she got my green/blue eyes and ended up with light brown hair and olive skin. I am confused because I thought darker genes were dominant and that she wouldn't be able to get any of my fairness. Please explain, as you can see I only have the most basic knowledge of this subject lol