You got that right. His church. According to his church.
But are any within his church infallible?
Are any in his church able to say infallibly that the Pope is infallible?
If they say that the Bible says infallibly that the Pope is infallible, how can they say that their interpretation of the Bible which leads them to believe that is infallible?
Yes, I believe in the inerrancy of the Word, and yes there are some things not up for dispute (that Jesus was virgin born, is the Son of God, was raised from the dead, etc) but some things (like this) are far from settled -— as the Pope is NOT Jesus.