The intrinsic stress in nanomultilayers (NMLs) is typically dominated by interface stress, which is particularly high in immiscible Cu/W NMLs. Here, atomistic simulations with a chemically-accurate neural network potential reveal the role of interfacial intermixing and metastable phase formation on the interface stress levels. These results rationalize an experimentally-reported compressive-to-tensile transition as a function of NML deposition conditions and the extremely high interface stresses under some conditions.