You husband cannot live or work "under" your green card. If you were married before you won the green card, your husband is eligible for his own green card. It will be better if he files his application together with yours.
If you won the DV lottery, the benefits also extend to your spouse and children under 21 years of age. They will need to submit their own immigrant visa applications or adjustment of status.
Your spouse can apply with you for the green card and should be able to work on the derivative green card he/she gets. We presume you listed your spouse on the Application when you made it.
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