I am sure a three-way mortgage is possible but be very sure you have reviewed this option carefully between yourseles before going ahead. What happens if one of you decides to marry and wants to take out their share of the equity towards a propery of their own? What happens if one of you wants to move a boyfriend in and how will this affect the dynamics of your arrangement? etc, etc.
You must get a watertight legal agreement drawn up, otherwise what looks like a easier way to get yourselves onto the housing ladder could end in tears.