Came vested all in white, pure as her mind; Her face was veil'd […] (9-10)
The speaker describes his wife as dressed in white and wearing a veil, and explicitly links her white clothing to her inner purity. The bridal imagery associates his wife with the chastity and innocence of a bride. Now that she is in heaven, the boundary between body and soul has collapsed so that his wife's virtues—in this case, her purity—are easily visible in her physical appearance.
[…] To my fancied sight
Love, sweetness, goodness in her person shin'd
So clear as in no face with more delight. (10-12)
The word "person" here represents some combination of body and spirit. So instead of being able to actually see his wife's facial features, the speaker sees her virtues—love, sweetness, and goodness—shining in her person. Frankly, if we could see virtues instead of, say noses, we wouldn't be complaining either.