Hi Myndy,
As Narendra has so well explained, there is no chance of having a thalassemic child, as long as one is beta minor and the other alpha minor. Two different genes are affected so there is no possibility of the two traits combining. However, as Narendra has also explained, you could have a thal child if one of you is a silent carrier for one of the traits. In addition to the expensive genetic testing, family histories are also taken into account. Relatives should be consulted on both sides to make sure there is no history of carrying the other trait in your families. This is especially important regarding alpha carrier status, as alpha is harder to detect with testing, so family history is extremely important when diagnosing alpha carrier status. You should talk to our family and see if there is any knowledge of alpha thalassemia trait in your family. If not, there is little likelihood that you would have any concerns.