OK, the way I see it ... he cares about you and the family and you care about the family. So, everyones heart is in the right place. Now, just try to get everyones brain going in the same direction. I'm a therapist so my sugestions will be somewhat psychobabblish but for what it's worth...
To ease the stress let your husband know what and how much you are eating, cal, fat, etc... give him as much info as you can. Explain to him what you are doing to ensure that you are not "starving". The kids need this info also. Spend time talking to everyone about healthy diets, explain that although you are cutting back you are having to choose healthy when you do eat. Everyone has to talk about their fears or this can snowball into a real big issue.