Interface stress is a fundamental descriptor for interphase boundaries and is defined in strict relation to the interface energy. In nanomultilayered coatings with their intrinsically high interface density, the functional properties are generally dictated by the interface structure, which in turn is governed by the delicate interaction of residual interface and volume stresses in the coating system. In the present work, experimental estimations of the interface stress in Cu/W NMLs (with a variable residual stress state from tensile to compressive) were compared with corresponding theoretical values as calculated using DFT (adopting an incoherent bcc W{110}/fcc Cu{111} interface with variable in-plane strain). The Cu/W interface stress was experimentally tuned monotonically from positive to negative values by changing the residual stress in the W nanolayers by increasing the Ar pressure during the W deposition steps. Qualitative agreement between experiment and simulation was achieved, both confirming a decrease of the interface stress from the compressive to the tensile regime. The DFT simulations showed that Cu atoms in the vicinity of the strained Cu/W interfaces are displaced along the in-plane and out-of-plane directions in response to the acting interface stress. Using a preliminary developed neural network potential for the immiscible Cu-W system, specific in-plane crystallographic orientation relationships for the Cu/W interfaces were also tested, which improved quantitative agreement between experiment and theory. Assumptions and limitations in experiments and theory for deriving the interface stress are critically discussed.