convertible mortgage=mortgage loan with lower interest rate + a call option on full or partial equity interest (from a lender's perspective)
Note: the lower interest rate on the mortgage loan is the cost of the call option, in return, the option allow the lender to convert its mortgage balance to equity ownership on the option's expiration date.
eg: CitiBank lends firm A a $70,000 convertible mortgage that allow CitiBank to convert the mortgage balance (or loan balance , means remaining loan) at the end of the fifth year to 70% equity ownership(equity interest) in the property. If at the end of fifth year 70% estimated sale price($750,000) of the property is greater than the mortgage balance($650,000), CitiBank would use this option to make profit, that is, this option earns $100,000(750,000-650,000) for CitiBank.
If the interest rate of conventional mortgage is 10%, CitiBank has to give a interest rate below 10%, say, 8%, to firm A on the convertible mortgage, the difference between conventional and convertible mortgage is just the "price" for this option.