This work is devoted to a special kind of capillary interaction, which differs from the common lateral capillary forces between floating particles. It appears between particles protruding from a liquid film and its physical origin is the capillary rise of the liquid along the surface of each particle. Special attention is paid to the case when the position of the contact line is fixed. The resulting capillary force is compared with that at fixed contact angle. It is demonstrated that the two alternative approaches to the calculation of capillary interactions, the force and the energetical one, are equivalent. When the liquid film is thin, the disjoining pressure affects the capillary interactions between particles attached to the film surfaces. The appearance of this effect is studied quantitatively for two specified systems modeling globular proteins in aqueous film on mercury substrate and membrane proteins incorporated in a lipid bilayer. For both systems the capillary forces appear to be strong enough to engender two-dimensional particle aggregation and ordering. This is a possible explanation of a number of experimental observations of such effects.