Well,
If you are going to use both eyes open, you'll need to learn to make use of your peripheral vision skills.
If you are attempting to shoot bullseye style, lining up the sights, going for extreme accuracy, you'll use your dominant/and or master eye, closing the non dominant/and or master eye to do so. To attempt to align the front and rear sight, and then superimpose that "sight picture" onto the target with both eyes open is making the mission more difficult than it has to be.
I can use both eyes open and align the sights in my peripheral, while looking directly at the threat, but it takes practice, and is just something I've developed over the almost 30 years of using peripheral vision of the gun and focusing on the threat/target.
Jim Gregg's chapter on eyes is the best written I've ever seen where shooters are concerned.
http://www.jimgregg.net/
Many people answering here and others who shoot handguns/longguns do not fully understand that you aren't necessarily or automatically born with a dominant side, that the eyes dominance can be very slight [ almost nuetral ] to extreme [ master ] in nature.
One needs to really understand their particular situation and relevant eye situation to be able to make use of their particular set of circumstances where shooting is concerned.
I'd suggest getting Jim's book to fully understand this situation. It will help you immensely in the future.
Brownie