"They" generally works, it's just not commonly used and so sounds a little odd. Try using "they" instead of instead of "he" and "her" for a few minutes to see. It works.

the Swedes have adopted the pronoun "Hen" [1] for exactly these purposes, to much global controversy.

[1] http://www.huffingtonpost.com/2013/04/11/swedish-gender-neut...

"They".