ubhato-bhāga-vimutta: the 'both-ways-liberated one', is the name of one class of noble disciples (ariya-puggala, q.v.). He is liberated in 2 ways, namely, by way of all 8 absorptions (jhāna, q.v.) as well as by the supermundane path (Sotāpatti, etc.) based on insight (vipassanā, q.v.). In M. 70 it is said:

''Who, o monks, is a both-ways-liberated one'? If someone in his own person has reached the 8 liberations (absorptions), and through wise penetration the cankers (āsava, q.v.) have become extinguished, such a one is called a both-ways-liberated one.'' Cf. D. 15.

 In the widest sense, one is both-ways-liberated if one has reached one or the other of the absorptions, and one or the other of the supermundane paths (cf. A. IX, 44).

The first liberation is also called 'liberation of mind' (cetovimutti), the latter liberation through wisdom' (paññā-vimutti).

 The first liberation, however, is merely temporary, being a liberation through repression (vikkhambhana-vimutti = vikkhambhana-pahāna: s. pahāna).

Buddhist Dictionary, Manual of Buddhist Terms and Doctrines, by NYANATILOKA MAHATHERA

ubhato-bhāga-vimutta

(Pāli, one who is liberated in both ways). A person who achieves liberation in two ways, namely by liberation of mind through the trances (ceto-vimutti) and liberation through insight (paññā-vimutti). It is possible to attain liberation by insight alone, but to perfect both methods is superior. The Buddha was one ‘liberated in both ways’. See also Vimutti.

A Dictionary of Buddhism, Oxford University Press, 2003, 2004 (which is available in electronic version from answer.com)