I would like to donate a house to charity, but we still owe on our mortgage. Is it still possible to donate?

Nope, you can't give away something that isn't yours, it has a lien.

I admire the spirit to give, one can not give what is not their's to give.

You may be able to Donate the Mortgage.

You could sell the house for the exact amount of the mortgage to the charity and in effect give them your equity