Very tricky - you would be buying a specified and predetermined share each, lets say 50/50.
Theoretically this can be done, but the mortgage company wil be very wary. If one of you defaults then the mortgage company couldn't repossess because of the other's rightful occupation.
Yes you can have two mortgages (or more) on one property, however there is an order of priority and the second lender would be in a far worse position that the first lender.