So is the Episcopal Church Protestant or Catholic?

Both. Neither. Either. Anglicanism is often referred to as a "bridge tradition." When the Church of England separated itself from Rome, it did not consider itself to be a "Protestant" tradition. Rather, it saw itself returning to the original organization of the church, with local/national congregations organized under the rule of their own bishops. As the church evolved in England, certain elements of the Reformation (such as worship in the vernacular, an emphasis on Scriptural authority, and a broader view of what happens during the consecration of the Eucharist) became a part of its tradition. In an attempt to reconcile the views of the Reformers with the tradition of the Catholic Church, the Anglican tradition became a home for both. Thus, while you will find very traditional ("high church" or "Anglo-Catholic") parishes and very reformed ("low church" or Evangelical) parishes, most probably fall in the middle of the two extremes.