ok, given two wires. what did you use as a reference to measure the voltage? what I mean is what did you use as a common to each wire?
what you are reading is the path of current from the transformer through the remainder of the circuit to the other side of the transformer.
Never use a digital meter for voltage measurements like this. An analog meter works better.
anyway, look through this forum. I made up a diagram for another person on how to connect up a doorbell.