how do I know or find out who backs my mortgage?

The vast majority of all home mortgages in this country are owned by FNMA or FHLMC and serviced by banks. Banks may also have some that are not FNMA or FHLMC owned that are referred to as Portfolio Loans because the bank owns them. This information can be helpful to determine if you qualify for a Home Affordable Refinance Program (HARP) loan. I am sure US Home Mortgage would be happy to tell you if you asked, but I have posted links below that you can use to search for yourself.

http://www.fanniemae.com/loanlookup/

https://ww3.freddiemac.com/corporate/

I don't think you understand what you are talking about. Fannie and Freddie back mortgages on the secondary market, which has no implication on the borrower. It is completely an issue between the bank that originated your loan and how it was sold on the secondary market in the form or a security. Your only concern is repaying the loan to the bank that is servicing your loan. Your original lender, nor the bank who is servicing your loan has no responsibility to inform you how your loan was treated on the secondary market as you are not a party to the transaction.

But if your loan was insured by FHA or VA, you would already be aware of this

Your mortgage company has no reason not to provide that information but if you look on the copies of your mortgage papers it should indicate if it is an FHA approved loan.

...by asking