Hi Judy,
The denial is quite common (many parents feel some guilt about passing on these genes, but how would you know? You wouldn't, so please assure your husband of this fact). Do you have any records of the test that he did have and do you know what his hemoglobin level is? Alpha thal carrier state is very difficult to diagnose without a DNA analysis, so it may be an educated assumption that this is alpha thal minor, based on the results of a complete blood count. If his Hb level is unusually low, then I would definitely suggest a DNA test.