Foreigners can be covered with the NHI (National Health Insurance Corporation) program on
a voluntary basis on the condition that they satisfy some requirements for their coverage.

The insurance benefits for foreigners are all the same as those for the Korean nationals.
When the insured person or the dependents get health care services at health care facilities, just like Korean enrollees, they should pay a certain amount of co-payment for the services covered.
The contribution amount shall be calculated by monthly salary contribution rate currently 4.77% and 2.38 % will be deducted from employee's monthly salary. (50% of which is shared by the employer). Irrespective of the actual date of enrollment, the obligation of contribution payment is retroactive up to the date the enrollee was employed.

The health care benefits include diagnosis, test, drugs, medical materials, treatments, surgery, preventive care, rehabilitation, hospitalization, nursing and transportation. When receiving health care treatments, the insured and dependents pay part of the health care charged based on the predetermined cost-sharing percentage or fixed amount. The services not considered necessary for activities in daily life, e.g. plastic surgery are not covered by the NHI program.

For outpatient services provided at a clinic, the patient must pay 3,000 won when the total charges do not exceed 15,000 won (at a dental clinic: 3,500 won) For more detail, please call or visit website.

Tel: (82)3270-9386~9
http://www.nhic.or.kr/wbe/nation/nation06.html

Otherwise employer can provide private insurance such as Samsung insurance or ING insurance.
Here are website of these insurance companies.

http://www.samsunglife.com/global/index.html
http://www.inglife.co.kr/index.jsp