The way I understand it, 何{なん}でもない and 別{べつ}に are both ways of saying "It's not important", "It's nothing" i.e. brushing off the question being asked. Does this mean that they are interchangeable? Or are there certain contexts where 何でもない is used and 別に cannot be and vice versa?
For example, in episode 19 of Revolutionary Girl Utena, the character Wakaba is asked by another character "Why do you keep accusing me of [being a player]?" to which she starts to reply, but then decides against it, saying "別に...何でもない" and turns away. In this context, she uses both, which makes me think that she uses both as a way of reinforcing "It's not important", which makes me think that both expressions have similar meaning and are therefore interchangeable.