Multilayered Cu-Ni has a peak yield strength four orders of magnitude higher than either Cu or Ni because the multitude of interfaces obstruct glissile dislocations. The barrier strengths of the interfaces may be traced to four mismatches across an interface: modulus, lattice parameter, chemical and slip geometry. This paper describes sample embedded atom method (EAM) simulations of dislocations crossing interfaces, designed to separate the effects of the four mismatches. The results confirm some classical calculations and emphasize the importance of three new effects (i) an interface-chemical effect in which dislocations are trapped by core spreading in the interface, (ii) a coherency-chemical effect caused by coherency strains changing effective stacking fault energies and (iii) a coherency-modulus effect in which coherency strains change elastic moduli (and hence the Koehler stress) significantly.