Suppressing staff households for snail mailings?

I've noticed an issue that staff households are being pulled into snail mail extractions. Our organization is in Tessitura with an organization type, and relevant individuals are affiliated as employees to our organization.
In extraction manager it's easy enough to create a suppression of all employees associated with an organization. The issue is that I don't know how to also suppress the households they are a part of based on the individual being affiliated as an employee. In the diagram below, I'm trying to suppress the items circled in red based on the organization.