Is black hair dominant over red hair?

Yes black hair is dominant to red hair, so it is most likely that your child will have black hair. Your husband's genes with regard to hair is fully recessive, so really the outcome of the hair color is dependent upon your genes. If you carry only the genes for black hair, it is 100% certain that your child will have black hair. However, if you carry the recessive gene for red hair, then your child has a 50% chance of having red hair.