Nice to see new people joining my chess riddles! :)

OK, lets look at your suggested moves (black's moves are always in the right column):

1. ... Rxh4+
2. Kg1 Rh1+
3. Kf2 Rxb1

But now white can give a check with:

1. Rf6+ Kg7
2. Rxd6

And it's white who wins ...

You need to find something better! :)