Brother go ahead !! Love Conquers all since God is LOve. BUt worry not, because it is not a necessity or requirement or any legal issue if you have different religion.

If you are both adults, Simply go to both embassies, and fill up the necessary forms to go ahead with the process. and presto !! you are both married.

later on, you can both decide which religion to follow.
Religion should never be a hindrance to love, it should bind us all.