Hello @TONY and welcome to our community!
I’m not really familiar with marriage law in the US, but I’ll try my very best to give you an overview based on my research.
In general it’s possible for your future husband to come to the US (with a visa) after receiving his blue passport - even if you are not married yet. He can obtain a visa to come to the US and marry you there within 90 days (that's a so-called "fiancé-visa"). Since he already received a positive result on his asylum case by BAMF, it shouldn’t take long to get the passport.
These websites provide a summary of all the information that is required in this case:
In theory, this doesn’t seem to be a complicated procedure. But to be honest, I can’t tell you in how far the travel ban or the Iranian nationality of your fiancé will turn into an obstacle in this case.
However, if you decide that it’s easier for you to get married in Germany, you will find some helpful information about similar cases here on the platform. Here is a short summary of things to keep in mind:
To get married in Germany you two need to provide a couple of documents. These include a valid passport, a birth certificate and a certificate of no impediment (to attest that you are eligible to marry and most significantly, to proof that you are not married or not married anymore). Both of you may need to provide further documents according to the marriage laws of your home country. It’s probably best to get in contact with the competent registry office (“Standesamt”) in your fiancés city to find out what documents exactly they need.
If you get married in Germany and you want to live together in the US, the procedure stated in the first part of my answer doesn’t apply anymore (since you are not fiancés anymore, but spouses aka family members). You will find answers on how to proceed in this PDF:
I hope this answer was helpful to you. Feel free to ask further questions if necessary.