Bisexuality?

In recent years I've come to the realization that I like girls and boys. I feel terrible about this because it breaks my moral code because I've been in a wonderful relationship for almost 3 years now. My partner knows that I am also interested in girls, which makes him insecure. I feel horrible when I mention it because I honestly don't have anyone else who can accept me as I am. I strongly believe in one man and one woman but the physical attraction I have for women is intense. I strongly believe that if I wasn't with my signifigance other, I'm certain I would be a lesbian. However, I love my significant other. I could never leave him or betray him. He is truly all I have and could ever need in this life. I just feel so awful because I can't help and stare when a beautiful girl walks by. I can't help but wonder what it would be like to feel their soft skin brush up against mine. I'm just very lost and confused and if anyone has advice on this I would greatly appreciate it.