If you report one schedule C, you will be telling the IRS that one spouse works and the other does not (unless the other spouse also has a regular job or is already retired). This could affect your eligibility for the child and dependent care credit (if you pay for day care), and may affect your ability to contribute to a retirement account or other tax situations (I'm less sure of that, the rules are tricky.)
You will also be telling the social security administration that only one of you is working, so only one of you will earn social security credits (unless the other spouse has a separate job). This will affect the other spouse's eligibility for retirement and disability pay.
If this was not a close relative helping but a third person, you would be expected to either issue them a 1099-MISC for their income or make them a W-2 employee. I think you can get away with one schedule C in the situation you describe where the spouse is an unpaid helper (rules for family are a bit more lax). But do be aware of the implications I mentioned above.
