Wiring a Doorbell System (NEC 2002)
It needs to be in a location where wiring can be run to it. Three terminals on the chime are labeled F, T, and B, which represent the front door, back door, and transformer. If you are going to run two separate circuits you will need a double pole switch.
Step 2 - Turn Off the Power It's essential that you turn off the power to the applicable circuit that will power the transformer. The issue with your diagram is that the button momentary switch that you are working with is a single pole switch.
How to Wire Two Doorbells to One Transformer - We are glad to have you as a member of the community and part of our online Home Depot family. In the wiring options above 2 wires are connected to each door button, To extend to another front button or another rear button connect another 2 wire cable to run from the 1st button to the 2nd button.