This thread is old, but I stumbled across it tonight. The village you are looking for goes by many names, depending on the era:

Austria, Galizien, Biała (Czortków) - Up to 1920's
Poland, Tarnopol, Biała (Czortków) - 1920's to WWII
Україна, Тернопіль, Чортків, Біла
Ukraine, Ternopil′, Chortkiv, Bila - post WWII

The Greek Orthodox records are on microfilms 2350947, 2349694 & 2349693. These microfilms are currently at the Los Angeles Family History Center. I placed them on extended loan because I found 40 ancestors on those films! I have been through them several times, but they are here in case I need to refer to them again. I have a special place in my heart for these films, as they answered a lot of huge questions in my family tree.

The Roman Catholic microfilm records are also on film 2350947. If you'd like to order this film and scan through it, I will let my local FHL center know that I don't need it anymore. I'm not sure how this works though.

OR, I could look through it for you. It's in my local library, I have a lot of experience reading these records (they are in latin & Ukrainian). I will attach a sample so you can see what I mean!

Happy to help another Bila descendant!
Steve