There is also the passage,
May your whole spirit and soul and body be preserved blameless at the
coming of our Lord Jesus Christ [1 Thessalonians 5:23].
The Orthodox Christian teaching on this - which is aligned with that of the Church Fathers - is that man comprises body and soul; and that the spirit is not distinct from the soul, but is, rather, the highest part of the soul and the faculty which knows God and enters into communion with him. At some point, the Fathers began using the Greek word νοῦς [nous] to refer to spirit in this sense, as distinct from soul - ψυχή [psyche].
The Patristic teaching is summarized in John of Damascus' Exact Exposition of the Orthodox Faith:
The soul, accordingly, is a living essence, simple, incorporeal,
invisible in its proper nature to bodily eyes, immortal, reasoning and
intelligent, formless, making use of an organised body, and being the
source of its powers of life, and growth, and sensation, and
generation, nous being but its purest part and not in any wise alien
to it; (for as the eye to the body, so is the nous to the soul) 
Other Patristic writers who showed the same understanding of the relation of spirit with soul include Justin Martyr, Irenaeus, Gregory of Nyssa, and Ephraim the Syrian.
 John Damascene. (1899). An Exact Exposition of the Orthodox Faith (S. D. F. Salmond, Trans.). In P. Schaff & H. Wace (Eds.), Vol. 9b: St. Hilary of Poitiers, John of Damascus (P. Schaff & H. Wace, Ed.). A Select Library of the Nicene and Post-Nicene Fathers of the Christian Church, Second Series (31). New York: Christian Literature Company.