The specification describes techniques for soldering IC chips, or other components, to interconnection substrates using a patterned epoxy layer to define the solder interconnections. The epoxy layer is photodefined to form openings that expose the bonding sites on the IC chip (or alternatively the interconnect substrate). Solder paste is deposited in the openings. With the IC chip and the interconnect substrate aligned together, the solder paste is heated to reflow the solder and solder bond the IC chip to the substrate. Heating is continued to cure the epoxy, which serves the function of the conventional underfill. The shape of the solder interconnection is defined by the lithographically formed openings, and the interconnections can be made with very fine pitch. The application of the epoxy underfill in this manner assures complete filling of the gap between the IC chip and the interconnection substrate.