Hb H disease is three gene deletion in the alpha hemoglobin genes. There are four alpha genes and when three are deleted, the symptoms can vary from mild to moderate anemia. Folic acid is always recommended.
With alpha thalassemia there is a danger if both parents are carriers. If both parents carry at least two of the genes (you carry three), then there is a danger of all four genes being alpha thal. This is a severe condition known as Alpha Thalassemia Major or hydrops fetalis. The child is usually stillborn. Recent preemptive treatment using prenatal transfusions is the first hope for survival in these cases.
Your wife is being tested because of this possibility. If she is a carrier there is a chance of all four genes in the fetus being alpha thal. If she has one or no alpha genes there is NO chance of having a major. The baby will receive one or two alpha genes from you and the other two genes come from the mom. The odds are not as high as you have been told of having a child with four alpha thal genes, but if your wife is a carrier there is that possibility. If she has never suffered from anemia, it is unlikely that she carries two alpha genes. Testing will tell, and the concern is most likely caused by the knowledge that you are HbH yourself.
You can read more about alpha thalassemia at
http://www.thalassemia.com/alpha_thal.html