I just joined, but I can't help to read your post and feel like I should help. My day job is a sex educator and so perhaps my credentials will help you believe the previous answer a little more. Only 23-27% of American women actually have an orgasm from sex. Many friends lie because like you they think it's not normal if they're not having an orgasm from sex. And by sex I mean the most common referred to action of penis in vagina. Sex to everyone is different and to some means no penetration at all, but from reading I think to you it means penetration.
Without understanding your body you're going to continue to be frustrated that you feel like you're not being normal in your sex practices. However if you had any idea how common it is for women to be frustrated like you because they are not having an orgasm with their partner inside of them you'd feel much more normal.
I would really recommend getting more comfortable with understanding how orgasm and your vagina works before working on it with your partner as a personal understanding helps in connecting with your partner much more. He's not very far off base asking for intimacy without orgasm. This is very common and can be acheived if you take the equation of sex and make it simpler. To some poeple sex starts from the minute they get up with a sexy note they leave for their partner before they leave for work, or a sexy text they send, or the fact that they went out of their way to grab something special for dinner because they knew their partner had a rough day. When you confine labeling "sex" to just when penetration occurs in the bedroom you restrict your mind and body to all kinds of experiences of intimacy and sensation and absolute wonderfulness that is waiting for you if you're willing to experience it. I'd strongly suggest reading I Love Female Orgasm and try reconnecting with yourself.