Thanks in advance.
The H-4 Visa
appears to be available to a spouse of individuals already holding an H-1, H-2, or H-3 Visa
, provided that you are able to prove that you are not inadmissible to the U.S. Accordingly, it may be wise, as a preliminary matter, to look into inadmissibility (likely to need government assistance, have committed crimes or security violations, spent too much time in the U.S. unlawfully, time-barred, have entered illegally more than once, have violated other immigration laws or fraud). Moreover, you have not clarified what type of permission your husband has that allows you to qualify for the H-4. Rather, it seems that he may be a permanent resident card holder (H Visas are for temporary visitors).
Moreover, you may wish to think about what you can do for income if living in the U.S., and how you can show that you do not plan to stay permanently yourself, as the H-4 may not permit you to work in the U.S. You can always apply for a different visa, of course.
Finally, if you are looking to apply for permanent residence, you may qualify as a “preference relative” (spouse of permanent resident card holder), however you may have to wait in line. Depending on demand, that may be years.
You should contact an attorney to further explore your options.