Depending on your contract with the secondary, the patient may or may not be responsible for more than $15.
No matter what, you cannot collect more from the patient than Medicare says you can, so in my world, the patient is responsible for $44. You cannot collect $44 plus $15.
I do not allow secondaries to "drive the bus"... they have to follow the rules of the primary. So in my world, the account would look like this:
Medicare deductible $135
Secondary paid............$91
Balance remaining... $44
Patient owes $44.
If you DO allow secondaries to reduce patient responsibility from the primary, then you would only collect $15 from the patient.