John Donne was writing at a time when the difference between Anglicanism and Roman Catholicism was largely a political one. Anglicans believed that the Pope was not the head of the Church; instead, the monarch was the head of the Church. As such, it is simpler to identify the ways in which Donne evidences a Christian faith in general in these two poems.
In Sonnet 10, "Death, be not proud," the poet's address to Death is based upon his belief that death is only a "short sleep" and that, after death, "we wake eternally." Although there is no mention of God in the poem, the basic premise of the poem is a Christian one. Donne is arguing that Death has no reason to be "proud" because he is less powerful than God and faith. Death is in fact subject to the whims of humans, who can cause each other's death with "poison, war and sickness." Death in fact only causes the faithful to sleep for a brief time, before they wake again to be with God.
Sonnet 14 makes more explicit reference to Donne's Christian faith, being addressed to "three-person'd God." This refers to the idea of God as a Trinity, or three beings in one, the Father, Son and Holy Ghost. Donne is appealing to God to "batter" him in order to make him new again. He declares that he loves God "dearly" but is "betroth'd" to his enemy, the Devil. The imagery, including words such as "divorce" and "ravish," suggest almost that Donne is in a romantic relationship with God but is constantly tempted by the Devil, another lover. He is begging God to "imprison" him so that he will not stray from him in future.