A quasi-three-dimensional analysis for an elastic crack at the interface between two semi-infinite dissimilar plates is conducted. The governing equations of the Airy stress function and the out-of-plane displacement are deduced based on the kinematic assumptions for quasi-three-dimensional deformation of plates in extension of Kane and Mindlin. It is found that the quasi-three-dimensional interface crack tip stress field is a complete combination of plane strain bimaterial singular field and antiplane shear singular field under pure tensile loading or pure in-plane shear loading. Three fracture modes are coupled together even if the oscillatory index ε (in plane strain or plane stress) is zero. The oscillatory behavior of the crack tip field is completely characterised by Dundurs' parameters in plane strain no matter how thin the plate is. The effect of plate thickness on stress intensity factors (SIF) is studied. In contrast to the plane stress solution, both the Mode I SIF under in-plane shear loading and the Mode II SIF under tensile loading are nonzero and can not be neglected in the nonoscillatory case. The Mode III SIF tends to zero when the nondimensional thickness h/a, where a is half the crack length and h is half the plate thickness, becomes vanishingly small and reaches its maximum at a certain value of h/a which depends on loading conditions. The antiplane shear effect may not be neglected for plates which are not very thin.