"Company" attributes should automatically flow to "Customers" (Employees)

We recently added a drop-down custom field to Company which we named "Industry." We made a drop-down list of most of the industries we do business with: schools, non-profits, etc. so we can market directly to those customers. 

I was pleasantly surprised to see that the new field shows up both for Companies and Customers. 

The trouble: When we assign an industry to a Company, it does not flow to that Company's customers/employees. So we then have to manually open each customer and assign the industry code.

I've tried it both ways:
- Assign a code to the Customer/employee, and see if it flowed to the Company (it did not)
- Assign a code to the company, and see if it flowed to the Customer/employee (it did not)

Hopefully you see the value in making just one entry and having the data filled in both for the Company and the Customer. 

BTW, I understand that this is my custom field and other users won't have this same scenario unless they've manually created it. But it seems that some info should be common for the Company and the Customer.