None of us are likely to tell you what you should or should not do other than to contact an immigration attorney. That said, your matter is serious and you should not look for too much direction from what is essentially a legal blog. Please, take the time to speak with someone about your particular situation.
The answer provided is general in nature and should not be construed as legal advice as not all facts are know by the attorney, nor does the answering of this question create an attorney client relationship.
An asylum claim is a difficult one to sustain. I understand the issues quite well and understand your fear. If you do decide to pursue a claim, you should definitely hire an immigration attorney to assist you. There will need to be some demonstration of the danger to you or your husband, due to the Sunni/Shia issue in Iraq. All the best of luck to you and your family.
This advice is general in nature and is not intended to create an attorney client relationship.
One can only apply for political asylum when physically present in the U.S. That's what you should do. But don't do that at the airport upon landing, since you will then be taken into custody and only released after establishing to have "credible" fear (could take weeks or even months in immigration (ICE) detention. Much smarter to apply for asylum affirmatively after having been admitted to the U.S.
Abroad one can only apply for "refugee" status at a US consulate or embassy abroad - a bad idea, since in all likelihood will be denied.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
You can apply for asylum from within the U.S. I would encourage you to find an immigration attorney with experience or at least a particular interest in what the basis of your claim appears to be, i.e. discrimination against Shia minorities in Iraq including intermarriage between Shia and Sunni, possibly someone with a background in/interest in Middle Eastern politics and possibly someone Arabic-speaking. I would be happy to answer any further questions you may have - inbox me if you like. Good luck!
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.