We place antiphons between the strophes of psalms when they are sung. This preference to doing so is in accordance with the General Instructions on the Liturgy of the Hours, which can be found on our web site at http://DivineOffice.org (look in the upper right corner of the page for the link). Here are a few excerpts from the General Instructions:
It is preferable to sing:
268 “The sung celebration of the divine office is more in keeping with the nature of this prayer and a mark of both higher solemnity and closer union of hearts in offering praise to God. . . . Therefore the singing of the office is earnestly recommended to those who carry out the office in choir or in common.” 
269 The declarations of Vatican Council II on liturgical singing apply to all liturgical services but in a special way to the liturgy of the hours.  Though every part of it has been revised in such a way that all may be fruitfully recited even by individuals, many of these parts are lyrical in form and do not yield their fuller meaning unless they are sung, especially the psalms, canticles, hymns, and responsories.
270 Hence, in celebrating the liturgy singing is not to be regarded as an embellishment superimposed on prayer; rather, it wells up from the depths of a soul intent on prayer and the praise of God and reveals in a full and complete way the community nature of Christian worship.
Antiphons are designed for use between each strophes especially when sung:
114 The antiphons in the psalter have been designed to lend themselves to vernacular translation and to repetition after each strophe, in accordance with no. 125...
125 In addition, when the literary genre of a psalm suggests it, the divisions into strophes are marked in order that, especially when the psalm is sung in the vernacular, the antiphons may be repeated after each strophe; in this case the Glory to the Father need be said only at the end of the psalm.
A new emphasis is being placed upon singing in the Liturgy of the Hours and of the Mass with the New English Translation of the Roman Missal. We have embraced the direction of the Church and are singing as many of the Hours as possible on days of higher solemnity, such as Sundays. We understand that most people are not accustomed to singing of the psalms, canticles, responses, etc., and so we are only doing so on these days of higher solemnity.