According to the Center of Applied Linguistics, "Two-way immersion programs strive to promote bilingualism and biliteracy, grade-level academic achievement, and positive cross-cultural attitudes and behaviors in all students."
Here is a national list of Dual Language Programs with Korean as the second language:
Denker Avenue School
Gardena, CA
Language used: Korean
Basic model: Minority language dominant
Contact: Marsha Schwab Thomas
Phone: 310-327-9420
Peary Korean/English Dual Language Program
Gardena, CA
Language used: Korean
Basic model: Middle or High
Contact: Jiah Kim
Phone: 310-225-4200
Foreign Language Academy of Glendale (FLAG) - Korean
Glendale, CA
Language used: Korean
Basic model: Balanced
Contact: Naehi Wong
Phone: 818-244-2113
Cahuenga School "Korean/English Dual Language Program"
Los Angeles, CA
Language used: Korean
Basic model: Minority language dominant
Contact: Jee Sun Chung
Phone: 213-386-6303
Flushing, NY
Language used: Korean
Basic model: Balanced
Contact: Betsey Malesardi
Phone: 718-463-3747
Claire Lilienthal Alternative School
KIP Program
415-750-8603
3950 Sacramento Street
San Francisco, CA
More information can also be obtained here.