You need to consult with an experienced immigration attorney who can review your history fully. Because of your asylum history and your husband's H1B, there are specific matters which need to be reviewed, and should not be done on a public forum like AVVO. Make an appointment to spaek with an attorney in the orivacy of his/her office so that your situation can be properly assessed and you can get propoer advice.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. A consultation with an experienced attorney is always the best way to go.
There is alway a chance of receiving a Request for Evidence in any immigration matter.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Because you are dealing with two very different areas of law, you are best advised to consult with an experienced immigration attorney who can take the time to help review your options under both the asylum and employment based green card aspects. Unfortunately in this unstable economic climate, an RFE for employment based cases is quite common.
You need to consult with an attorney to find out whether you are or will be eligible to help your husband obtain permanent residency based on your status. He will need to work closely with his company's attorney regarding the perm process, which is lengthy and complex.