@oristarA,
"Mainline" refers to a group of protestant denominations (i.e. christian groups with a distinct set of doctrines and practices). It may imply that these are the denominations that are "moderate", respectable and not extreme in any way.
It is an odd term though because of the hundreds of different Protestant denominations, there isn't really a clear line between evangelical churches and mainline churches. Many people consider themselves both evangelical and mainline.