Hönisch was born in Habelschwerdt, Silesia, now in Poland. He attended a Jesuit grammar school and entered the Society of Jesus in 1952. From 1958 to 1960, as a scholastic, he was in Japan under the then-provincial Pedro Arrupe, SJ. He returned to Germany for health reasons, and in 1963 he was ordained a priest by the bishop of Berlin, Archbishop Alfred Bengsch. He finished his tertianship in Paray-le-Monial, and was first appointed chaplain at a Berlin grammar school, then parochial vicar of a parish in Gießen, Hesse.
While at this post, in 1976, Hönisch co-founded the Catholic Scouts of Europe (KPE). His teaching and youth work brought him into conflict with his superiors, which led to his expulsion from the Society of Jesus. He was also a gifted musician, organ player and choir director, and later said that he was unable to sing for one year following his expulsion.
He was incardinated as diocesan priest into the diocese of Augsburg, Bavaria. With the consent of the bishop of Augsburg, Monsignor Josef Stimpfle, he founded the new order of the Servi Jesu et Mariae (SJM, Servants of Jesus and Mary) in 1988. The first members of the order came from the Catholic Scouts of Europe founded by Hönisch. The SJM were recognized as a Congregation of Papal Right in 1994. The congregation runs a boarding school in northern Germany and is engaged in the Pastoral care of the Katholische Pfadfinderschaft Europas.