hi,
your situation is not really clear in details, but in general: if your husband is an asylum seeker, it means, that he has still any residence and job permission for working in Germany. In this case he has to apply for the job permission to the Ausländerbehörde using the company contract. It usually takes 4 weeks or longer to get the permission to work in this company. There is any other way to work legally in Germany. I'd like to suggest to you to talk to the company and said, that you have to apply for the job permission. You can also ask to a legal conselling if your husband can makes an internship in the company wihtou any permission from the migration office. It depens on his legal status but usually you can make an internship for 3 months without pay (Mindestlohngesetz). I'm not sure, if that will a good step in to the company anyway. At best you **** for a consulting office in your city of residence. If you are in Berlin, you can come to the LernLaden Neukölln in der Karl-Marx-str. 131 every day at 9 or am tuersday at 14.
Best regards