As Hebrew Catholics we observe the Hebraic traditions of our ancestors along with our Catholic faith. We are fully Jewish and fully Catholic. We are in full communion with Pope and faithful to the Magistrate. Our beliefs are not different than other Catholics, but our traditions differ, along with our liturgical works and calendar.
Hebrew Catholics do not form a schismatic sect within the greater Catholic Church. We are similar to any ethnic church or sui iuris (Eastern Catholics, Byzantines, Ukranian Catholics, etc.)
The Mass at the hermitage in Belen is said in Hebrew with portions in Aramaic and English.
We don't force our traditions on others and we are not attempting to create a "sect" within the Church, contrary to what some sedevacantists claim. Such individuals are false Catholics who have chosen to remain separated from the Pope.
Saint James Vicariate for Hebrew Speaking Catholics in Israel
http://www.catholic.co.il/
Hebrew Catholics in Israel
http://www.catholim.com/
Association of Hebrew Catholics
http://www.hebrewcatholic.org/
Hebrew Catholics article on Wikipedia
https://en.wikipedia.org/wiki/Hebrew_Catholics
