If you are installing 2 doorbells (or a doorbell and a buzzer) the units should be in parallel, not in series. However, there are a couple of other caveats to understand as well:
1) This will only work if the current doorbell is a mechanical unit (actual sound bars being struck to create the ding-dong sound). If you have an electronic doorbell with a speaker, then a diode will be installed on the push button and the buzzer will sound continuously when connected. It will quickly be permanently damaged.
2) With 2 units, the current transformer may not provide sufficient output power. With 2 doorbells we recommend stepping up to a 16VAC 15VA transformer.
You could also consider using purchasing the DL-6157 Wireless Doorbell Extender. This kit comes with an extender component that you place on or near your existing doorbell, and a wireless plug in doorbell that you would place downstairs. When someone rings your doorbell, the extender component sends a wireless transmission to the plug in doorbell and causes it to ring as well.
If you have any additional technical questions, please feel free to call the Heath/Zenith technical service department at 1-800-858-8501.