Yes, it can be split if you like and each spouse will have their own schedule C. Its called a Qualified Joint Venture. The main benefits are that both spouse's have income (needed for some credits like the child and dependent care credit) and both are contributing to social security and medicare. You can just split the 1099-misc down the middle and add it in the income section (a few screens after the 1099-misc screen) and keep the 1099-misc for your records if the IRS asks about it.
Here is some information on qualifying for the Qualified Joint Venture:
https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Election-for-Husband-and-Wife-Uninco...