If you're paying the full bill in QBs, then you need to account for the full bill in QBs. You just can't have 10% floating around and not accounted for. (Can't do that even if you were doing paper ledgers!)
Not sure if this is the best way, but to specifically answer your question, you would show a split in the payment to three accounts. And I'm going to "assume" that you really mean you have two companies with their own Tax IDs, so you have two QBs Company files.
Payee: Cell Phone Company $100
Account: Office Expense: Cell 75
Account: Company 2 Liability 15
Account: Owner Equity 10
The Company 2 Liability Acct will now have a balance in it. You can pay Company 2 monthly, quarterly or whenever you want (or your Accountant wants).
Payee: Company 2 $15
Account: Company 2 Liability 15
Your portion will be shown in Owner Equity... Or again, wherever your Accountant wants it to be shown.
I personally would just ask your accountant if Company 1 should just pay the cell bill and be done with it. Or split it between the two companies. If you're *really* only using your phone for 10% personal, then why even bother breaking it out. Equate it to the coffee and donuts the companies buy for the employees, or the Friday pizza, etc.
Guess a good gauge here would be... Do you have a land line? Or another Cell Phone? So how much "personal" use is there?? My company pays for my cell phone, and yes it is used mostly for business. But my Accountant breaks it out at tax time to what they think I can really call an expense and what is my usage. I don't bother with trying to do it every month. (And yes, I also have a personal home phone.)