With the correct configuration, everything will work as you expect.

I was confused by the part of your question where you discuss purchasing an inventory asset but also showing an expense. 

You can EITHER expense inventory OR record it as an asset - not both at the same time.

• If you purchase the inventory and keep it as an asset to later sell it, you will report cost of goods at that time.

• If you purchase the inventory and expense it, you will report an expense, but there is no asset.

This example works through the funding and purchasing of a service instead, but it would work the same way with a purchase of inventory also (either expensed as you would for janitorial supplies for example or when it is recorded as an asset that you later sell and later record as a cost of goods).

1. If you purchase inventory to later sell, Company C would show an inventory balance on the Balance Sheet, later moving to a cost of goods balance on the Income Statement.
   

2. If you purchase inventory to expense, Company C would show an expense balance on the Income Statement (like this example).

First, setup DUE TO and DUE FROM accounts to manage the Inter-company Receivable and Payables:

Then, configure each Company record (in EACH of Company A, B and C) to use these accounts instead of the defaults:

Now, you can record the funding scenario you describe.

In Company A’s books:

Send funds to Company B with a Customer Payment:

In Company B’s books:

Receive funds from Company A with a Vendor Payment:

Send funds to Company C with a Customer Payment:

In Company C’s books:

Receive funds from Company B with a Vendor Payment:

Assuming Company A had $500 to start with, this is the Balance Sheet at this point:

Company A: has $400 in the bank and is owed $100 from Company B.

Company B: has $0 in the bank (it went straight through), is owed $100 from Company C and owes $100 to Company A.

Company C: has $100 in the bank and owes $100 to Company B.

If Company C then incurs an Expense from a Vendor, it will show up ONLY on their Income Statement.  There has been no income or expenses in the other Companies at this point and their Income Statements are blank.

At this point, the LIABILITIES section of the Balance Sheet would then look like this:

The only change here is in Company C:

Company C: now owes $100 to a Vendor as well as owing $100 to Company B.

If Company C then PAYS that expense, the Balance Sheet for all three Companies now looks like this:

Again, the only change here is in Company C:

Company C: now has no money in the bank, and still owes $100 to Company B, remember they have a $100 expense on their Income Statement.