Abstract A general and systematic procedure is developed for calculating the hydrodynamic force and torque experienced by an arbitrarily-sized, -shaped and -oriented particle undergoing an arbitrarily-directed translational and rotational motion inside one of two semi-infinite immiscible fluids separated by a planar interface. The procedure is developed for the case where the ratio, K, of particle characteristic size, a, to the particle's characteristic distance, d, from the interface is much smaller than unity (i.e. K ⪡ 1). Situations in which the far fields in each of the two fluids are arbitrary Stokes flow fields are also included in our analysis. Expressions derived for force and torque are in the form of a power series in the ratio K. It is demonstrated that the general results presented here can be easily used to derive explicit expressions for force and torque on any given particle in terms of the fluid and flow properties, as well as certain geometrical properties of the particle, provided the solution to a particle-dependent Fredholm-type surface integral equation is known or obtainable. The utility of the general results in calculating the hydrodynamic resistance of particles is illustrated by the example of an arbitrarily-oriented ellipsoid translating and rotating in a quiescent two-phase fluid. Applications to bodies, such as slender bodies, for which only an approximate solution to the integral equation is available, are also briefly discussed.