You could try it both ways but it is almost always better to file jointly. You should create 2 Sch C’s so that you each receive credit for your self employment tax which in part goes on your social security record.
Just because you were both self-employed, it doesn't mean that you should file separately.
You can fill out your returns both ways, married and separate, and go with the one that is more beneficial.
You can always file jointly when you are married, even if you have different kinds of income or different self-employment jobs. Just make sure to include a separate schedule C under the name of each taxpayer to report that taxpayer‘s separate job.
In rare cases, you might benefit by filing separately, but the only way to know this is to test it in your specific situation. For example, about 15 years ago, my wife and I discovered that if we filed separately, we would receive about $500 back from New York State although our federal refund was reduced by $200. But again, this is highly specific and only you can know for sure.
Remember that if you file separately, then both spouses must itemize their personal deductions on schedule A, or both spouses must take the standard deduction. You are not allowed to stack all of the itemized deductions (charity contributions mortgage interest and so on) onto one spouse and have the other spouse take the standard deduction.