"the mortgage is in both the partners names and the partnership's name"

That's typical for having the partners as individuals "co-sign" for the LLC borrowing, so that the lender has a fallback position to pursue repayment.

You don't seem to understand Basis. You didn't state what they paid for. The $700k is the Cost (Basis) for whatever they Got for the purchase and the borrowing is liability. They bought 'something' which is the asset; they might have assumed other outstanding liabilities and/or receivable asset. The Basis doesn't change or rely on how they paid or how much they paid at first, or if they paid in full or if there is also debt; it is a Known value (the Purchase) and then it becomes part of the math.

Basis in Assets purchased = cost

Any debt is entered

= Net equity is the final result.