This paper studies intersection and union type assignment for the calculus LambdaBar-Mu-Mutilde [Curien-Herbelin'00], a proof-term syntax for Gentzen's classical sequent calculus. Starting with the notion defined in [DGL-ITRS'04], System MIU, we show that this is neither closed for subject-expansion, nor closed for subject-reduction. We will present System MC, an extension of MIU (by adding typing rules), and show that it satisfies subject expansion. We also show how to restrict MIU so that it satisfies subject-reduction as well, but only when limiting reduction to (confluent) call-by-name or call-by-value reduction.