Yes. If you don't split up the income and expenses, then one of you will get all of the social security credits and the other one won't get anything.
The only reason to file two schedule C's is so that both spouses earn Social Security credits. Doing this is called a Qualified Joint Venture. You only receive Social Security credits with earned income. Schedule C profits are earned income. If both spouses work the same business, a QJV fits the application best. The spouses must share the items of income, gain, loss, deduction, and credit in accordance with each spouse's interest in the business.
