A structure theorem for most unions of complete intersections

Using the connections among almost complete intersection schemes, arithmetically Gorenstein schemes and schemes that are a union of complete intersections, we give a structure theorem for the arithmetically Cohen-Macaulay union of two complete intersections of codimension 2, of type (d1, e1) and (d2, e2) such that min[d1, e1] ≠ min[d2, e2]. We apply the results for computing Hilbert functions and graded Betti numbers for such schemes.