A church famed for its polyphonic and chant traditions and its support of the arts, it has taken the "Reform of the Reform" in a slightly different direction from places such as the Church of Our Saviour or St. Agnes in St. Paul, Minnesota, or perhaps it simply has not re-arranged their musical program or liturgy much since the earliest, tenative changes of Advent 1964.  A friend of mine once remarked, in describing their masses to me, as I have never visited, it was rather like time-travelling to a somewhat liturgically conservative parish in Europe circa 1965, an unsettled if historically interesting time to be sure; I say this not as a criticism but simply by way of explanation.  I believe they use the 1970 missal, but with a slightly different translation of the various dialogues between priest and people that, while closer to the original Latin, is still unofficial (for example, "And with your spirit.")  I do not condone this practice by any means, or other major deviations from the current translation (though I definitely understand the impulse behind it), but simply report it as a curiosity.  Nonetheless, whatever particular small deviations are present, I am told it still represents an example of dignified liturgy and world-class music, and am glad they have maintained their choral tradition with such scrupulous attention.
Holy Thursday, March 20
Mass of the Lord's Supper (bilingual) - 7:30 p.m.
Altar of Repose in the auditorium is open until 10:00 p.m.
Good Friday, March 21
Tenebrae - 10:00 a.m.
Celebration of the Lord's Passion (English) - 3:00 p.m.
Celebration of the Lord's Passion (Spanish) - 6:00 p.m.
Holy Saturday, March 22
Tenebrae - 10:00 a.m.
Easter Vigil - 7:30 p.m.
Easter Sunday, March 23
Masses - 8:30 a.m., 10:00 a.m. (Spanish), 11:15 a.m. (choir), 1:00 p.m. (family)
Corpus Christi's website also helpfully includes the following information on the music for the various Holy Week Liturgies:
Holy Thursday - Mass of the Lord's Supper
Gregorian chant:  Introit - Nos autem; Antiphons - Postquam surrexit Dominus; Ubi caritas;  Domine, tu mihi lavas pedes; Mandatum novum do vobis; Maneant in vobis; Communion - Hoc corpus; chant hymn during final procession - Pange lingua.
Agnus Dei: Missa In illo tempore, Claudio Monteverdi
Motets: Credidi propter quod locutus sum, à 8, Claudio Monteverdi; Pan divino, graçioso, sacrasancto, Francisco Guerrero; Ave verum, Harvey Burgett.
Good Friday - Tenebrae
Gregorian chant antiphons, psalms, lessons.
Motets:  Ludovico Viadana, Marc'Antonio Ingegnieri.
Good Friday - Solemn Liturgy of the Lord's Passion
Gregorian chant:  Gradual - Christus factus est
Passion of Christ from John's Gospel:  chant recitation in English with choral responses by William Byrd
Improperia:  Tomás Luis de Victoria
Motet:  O vos omnes - Richard Deering; Tenebrae factae sunt - Johannes Nucius.
Holy Saturday - Tenebrae
Gregorian chant antiphons, psalms, lessons.
Motet:  Ludovico Viadana.
Holy Saturday - The Easter Vigil
Gregorian chant:  Psalms & canticles, Easter proclamation- Exsultet,  Antiphon - Vidi aquam, Communion Pascha nostrum.
Agnus Dei:  Missa V, super Ecce quam bonum, Hans Leo Hassler
Anthem:  Salve festa dies,  Ralph Vaughan Williams
Motets:  Surrexit Christus hodie - Melchior Vulpius;  Surrexit Dominus - Jacob Handl.
Easter Sunday
Gregorian chant: Introit - Resurrexi; Gloria and Sanctus, Missa VIII De angelis
Agnus Dei:  Missa quatuor vocum, Domenico Scarlatti.
Motets: Sequence - Victimae Paschali, Eustache du Caurroy; Haec dies, Giovanni Pierluigi da Palestrina; Christ being raised from the dead -John Blow 
Organ chorale preludes for Easter from the Orgelbüchlein, Johann Sebastian Bach.