Here is the list of mainline churches & denominations:

http://www.theopedia.com/mainline-church

https://www.gotquestions.org/mainline-denominations.html

A little history of mainline churches: http://www.huffingtonpost.com/william-b-bradshaw/mainline-churches-past-pr_b_4087407.html

After 20 years, I resigned from the Presbyterian Mission. My resignation was accepted, but I was asked to continue as an affiliate missionary with the Presbyterian mission. I did this until 1977, when I realized that I would not be living in Korea again.” —Sarah Barry

Barry herself admitted that she and UBF broke off all ties from the Presbyterian church.

Quote Reference: http://history.ubfservice.com/people/sarah_barry/sarah_barry.htm