The challenge for many parents is not so much the usual difficulties with the language or acclimating to a new culture, but rather being afraid of what their children may be exposed to every day in the media and many schools, he said.
"This is the irony, that is the dilemma," he said. They escape from gunfire in Iraq trying to save their family so they go to the United States "and they find physical security, but then they face moral attack," he said.
Because of a lack of moral grounding in the wider culture, families turn to the church for help as they struggle to maintain their Christian identity and live according to the Gospel, Bishop Jammo said.
The bishop was in Rome for his "ad limina" visit to the Vatican together with other heads of Eastern Catholic dioceses in the United States.
Chaldean Catholics are the largest Eastern-rite community in the United States and their numbers are steadily growing. The Chaldean eparchies based in Detroit and San Diego count about 165,000 faithful, according to Vatican statistics for 2011.
Bishop Jammo said their growing numbers are due to a large and steady stream of refugees since the U.S.-led invasion of Iraq in 2003.
Chaldean Bishop Ibrahim N. Ibrahim, who heads the Eparchy of St. Thomas the Apostle of Detroit, the diocese for Chaldean Catholics in the Eastern United States, said the biggest challenge in his diocese is how to help families who have been unable to go to church for years.
Many of the refugees spent five to 10 years in a transit country such as Lebanon, Jordan or Syria before they found a home in the United States, he said.
The bishops' aim is to make them feel at home "after those years of suffering" and to help them acclimate to their new surroundings and reignite their faith, he said.
Many refugees have "become confused" in terms of their faith during their hiatus abroad, either losing their faith because they had little to no access to a priest or pastoral care or because they found solace in a Protestant community, he said.
"However, when they arrive in the States, we get them back" when they discover the large, vibrant Chaldean Catholic community, he said.
"They want to be with their own citizens, their own people, family and friends" and hear their own language, he said.
Bishop Ibrahim estimates there are really more than 180,000 Chaldean Catholics just in his eparchy alone. He said they have 1,100 baptisms and 400 weddings a year, which keeps their 20 priests very busy.
In each of the past five years, they have ordained one U.S.-born priest a year, but this year they will ordain two men.
"That is a good sign and I'm going to tell the pope (during their meeting May 18) that we are really blessed by the vocations of young people for the priesthood," he said.
For both bishops, funding new parishes and pastoral programs for their growing number of parishioners are enormous challenges.
Despite the generous help they receive from the U.S. Conference of Catholic Bishops, Bishop Jammo said the economic investment needed to fund Bible study programs, youth groups, catechisms, and provide for seminarians, priests, nuns and teachers is "overwhelming."
Many Chaldeans arrive in the United States with appropriate skills and education, and a desire to work, but there are no jobs, said Bishop Jammo. That means most parishioners are not only unable to help fund and support the parish and its work, they need financial and social assistance from the church, he said.
"I am racing against time because I don't want to lose even one soul," he said.
The Eastern Catholic bishops formed the last group of bishops from the United States making their visits "ad limina apostolorum" (to the threshold of the apostles) to pray at the tombs of the apostles Peter and Paul, to meet with Pope Benedict XVI and to visit Vatican officials to discuss issues of common concern.