If there are two separate 1099-MISC forms (one for you and one for your husband) I would enter them separately as two separate Schedule Cs on the Form 1040. However, if there is only one 1099-MISC, then enter that 1099-MISC under the social security number that it was issued to. The fact that you both use the same car is okay.

Another option would be treat your business as a "Qualified Joint Venture".  A qualified joint venture is a joint venture that conducts a trade or business where (1) the only members of the joint venture are a married couple who file a joint return, (2) both spouses materially participate in the trade or business, and (3) both spouses elect not to be treated as a partnership.

Spouses make the election on a jointly filed Form 1040 by dividing all items of income, gain, loss, deduction, and credit between them in accordance with each spouse’s respective interest in the joint venture, and each spouse filing with the Form 1040 a separate Schedule C (Form 1040), Profit or Loss From Business (Sole Proprietorship) or Schedule F (Form 1040), Profit of Loss From Farming and, if otherwise required, a separate Schedule SE (Form 1040), Self-Employment Tax. For example, to make the election for 2014, jointly file your 2014 Form 1040, with the required schedules (see below).

For more information see: IRS on Husband and Wife Business