The problem is that there are two different meanings to the word interface. There is the commoner meaning which means place or area where two things meet, and the specific meaning of the Java® interface keyword to mean a structure specifying behaviour but without an implementation. That latter changed in Java8.
I would say that the public interface of a class comprises its public methods and public fields and probably its public constructors. Of course, you will not normally have any public fields. Remember what the I in API means.