We pay 30% rent to the business issuing my husband's 1099. The 30% comes directly out before my husband is paid, so it does not show on the 1099. Can we deduct that?

Yes, you can deduct the 30% rent you pay since the 1099-MISC form shows 100% of the income your husband earned not the 70% he actually received. 

For additional information, see What self-employed expenses can I deduct? and 

Where do I enter my self-employment business expenses, like home office, vehicle mileage, and supplies?

no - because you technically never received the money to begin with, so you already have the benefit. 

if the rent was not netted from the 1099 (meaning the 1099 was a higher dollar figure) than you could, but it gets you back to the same place. 

@HelenC12  - can you please go back and read the question again and reconfirm your response.... the 30% comes out BEFORE the husband is paid, which I read as :

earned $100

rent     ($30)

1099 shows $70 

you CAN NOT deduct the $30 a second time.