Per the Website below, the warranty on the hybrid system on a 2010 Prius is 8 years/100,000 miles:
"Hybrid System Warranty: 96 months or 100,000 miles, whichever comes first. This warranty includes the Battery Control Module, Hybrid Battery, Hybrid Control Module, and the Inverter (with converter)."
I don't think the fact that your dealer performed recall updates negates the balance of your vehicle warranty.
You did not mention where you live or how many miles are on your Prius. I think the warranty is a little different in California, but I am unsure. Perhaps, California owners will provide additional warranty information.
How do you know the inverter is defective? Is that your guess, or did the dealer troubleshoot this problem? -- There are several other components that can fail and exhibit similar symptoms.
What were the exact symptoms exhibited when your car failed?
What are the fail codes that were generated?
Regarding your husband performing the repairs, it is unlikely that an individual lacking specific Prius maintenance and troubleshooting training can accurately diagnose and repair a hybrid system failure. Even if he is able to determine which part failed, working on the hybrid electronics involve high voltages that can cause severe injury and/or death by electrocution. Plus, any printed circuit boards and other Prius specific electronic components are only available through Toyota dealers or your local junk yard. Therefore, most repairs are best performed by your local Toyota dealer's service department.
If you purchased your Prius new from this dealer, and you have had all periodic maintenance performed in their service department; the service department manager and Toyota may be willing to offer a "good faith" discount on the parts and/or labor. For example, the traction (high-voltage) battery on our 2002 Prius failed last summer, and the dealer and Toyota absorbed $1,200 of the $3,100 total bill. In any case, it doesn't hurt to ask; all they can say is NO.
Awaiting further details on your failure...