  We show that odd-parity superconductivity occurs in multilayer Rashba systems
without requiring spin-triplet Cooper pairs. A pairing interaction in the
spin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state in
the magnetic field parallel to the two-dimensional conducting plane. It is
shown that the layer-dependent Rashba spin-orbit coupling and the orbital
effect play essential roles for the PDW state in binary and tricolor
heterostructures. We demonstrate that the odd-parity PDW state is a
symmetry-protected topological superconducting state characterized by the
one-dimensional winding number in the symmetry class BDI. The superconductivity
in the artificial heavy-fermion superlattice CeCoIn_5/YbCoIn_5 and bilayer
interface SrTiO_3/LaAlO_3 is discussed.
