If my husband says he has diabetes, is it right that he should not eat white rice and pasta?

Yes but! Rice and pasta are very high in carbohydrates and the carbs increase the blood sugars to very high level, that is why doctors ask to avoid these. But if u decrease the serving size and stick tono more than 45- 60 gms of carbohydrate per meal.
Yes. Rice and pasta are complex carbs and a general no no for diabetics. I tell my patients it's ok to eat just alot less!