Private institution of higher education means a not-for-profit educational institution located within this state which is not owned or controlled by the state or any political subdivision, agency, instrumentality, district, or municipality thereof, which is authorized by law to provide a program of education beyond the high school level, and which:

(1) Admits as regular students only individuals having a certificate of graduation from a high school or the recognized equivalent of such a certificate;

(2) Provides an educational program for which it awards a bachelor's degree; provides an educational program, admission into which is conditioned upon the prior attainment of a bachelor's degree or its equivalent, for which it awards a postgraduate degree; provides a program of not less than two years in length which is acceptable for full credit toward a bachelor's degree; or offers a two-year program in engineering, mathematics, or the physical or biological sciences which is designed to prepare the student to work as a technician and at a semiprofessional level in engineering, research, medicine, or other technological fields which require the understanding and application of basic engineering, scientific, or mathematical principles or knowledge;

(3) Is accredited by an accrediting agency or association or, if not so accredited, is an institution whose credits are accepted, on transfer, by not less than three institutions which are so accredited, for credit on the same basis as if transferred from an institution so accredited; and

(4) Has a student admissions policy that does not violate any other Nebraska or federal law against discrimination on the basis of race, color, creed, national origin, ancestry, age, gender, or handicap.