If the mother is alpha and father is beta thalassemic, can their children be free from thalassemia?

Only if traits: If mom and dad are both thalassemia trait, not "major", then mom and dad most likely each have one normal gene. The child who inherits the normal gene from mom and from dad, will end up with 2 normal genes and no thalassemia!

Too little info: Very complicated question. If dad has beta thal minor, children have 50/50 chance of not having beta. If he has beta thal major, all will have trait. Risk of Alpha depends on severity of mom's disease, but given the variation in the number and location of Alpha gene deletions that cause Alpha thal it's impossible to predict transmission without more info. Your doctor should be able to help.