He should be fine if he has the correct documetns including a current letter from your employer and your H1B approval notice and LCA. it would be helpful to know why the last petition was denied
Why was he denied the L1B? Assuming it was not an issue related to a previous immigration violation or something along those lines, of course he can join you as your husband/dependent, no need to wait!
He needs to take evidence of your lawful H-1B status in the U.S. (check embassy website or talk to your employer's immigration attorney).
To qualify for an H-4 visa stamp, he must demonstrate that you are maintaining H-1B STATUS, not that you have an H-1B visa stamp.
Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can find one through http://www.ailalawyer.com.
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.