The nominative form of pronouns is used following a linking verb. Thus "It is I" and "This is he." Linking verbs are verbs about being rather than action, eg is/am. This can sometimes sound stilted, but it's English. It's good to have high standards even if one can not live up to them.
Somewhat related is You and I versus you and me. It's easy to sort that one out without making any reference to grammatical terms. Just mentally simplify the sentence to one person and it clarifies itself. Eg, "You and me should have lunch." "Me should have lunch"? Naw. So it's "You and I..."