If you use online TurboTax you will need to use the Self-Employed version; if you use desktop software, you could use Deluxe or higher, since all of the desktop software versions have the forms and schedules needed. Your spouse will need to complete schedule C for his business expenses (mileage, etc.).
Tax Tips for Uber, Lyft, Sidecar and other Car Sharing Drivers FAQ
https://turbotax.intuit.com/tax-tools/tax-tips/Self-Employment-Taxes/Tax-Tips-for-Uber--Lyft--Sidecar-and-other-Car-Sharing-Drivers/INF28820.html