Yes - it is possible for a family trust to borrow to purchase a property in partnership with a related SMSF.  Under this type of structure the SMSF will not qualify for the borrowing exemption as prescribed by section 67A of the Superannuation Industry (Supervision) Act 1993. This effectively means that SMSF is unable to borrow in a partnership arrangement.

The above is reiterated by Regulation 13.14 of the Superannuation Industry (Supervision) Regulations 1994 (SISR) and the Australian Prudential Regulation Authority (APRA) Superannuation Circular No. II.D.6.

The APRA Circular states that it would be prudent for the SMSF to refrain from investing as a tenant in common where the related party intends to use its investment in the property as security against the borrowing.  However, it does not forbid it.

Whether you could find a lending institution that would accept such an arrangement is another issue for consideration.