We place antiphons between the strophes of psalms when they are sung.
The preference to do so is in line with the General Instructions of the Liturgy of the Hours, which can be found on our web site at https://divineoffice.org/general-instructions. Here are a few excerpts from the General Instructions:
It is preferable to sing:
268. “Sung celebration of the Office, because it is more in keeping with the nature of this prayer and is a mark of greater solemnity, and the expression of a deeper union of hearts, in offering praise to God, is earnestly commended to those who perform the Divine Office in choir or in common.” 
269. The declarations of the Second Vatican Council on liturgical singing apply to all liturgical actions 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: above all, the psalms, canticles, hymns and responsories.
270 Hence, in celebrating the liturgy singing is not to be regarded as an extrinsic embellishment to 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 perfect 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; they are also constructed for repetition after each strophe, in accordance with no. 125. [...]
125. In addition, when the character of a psalm suggests it, the divisions of the strophes are indicated, in order that, especially when the psalm is sung in the vernacular, the antiphons may be repeated after each strophe; [...]
Greater 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.