  We construct families of symmetric, antisymmetric, and asymmetric solitary
modes in one-dimensional bichromatic lattices with the
second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair
of sites placed at distance $l$. The lattice can be built as an array of
optical waveguides. Solutions are obtained in an implicit analytical form,
which is made explicit in the case of adjacent nonlinear sites, $l=1$. The
stability is analyzed through the computation of eigenvalues for small
perturbations, and verified by direct simulations. In the cascading limit,
which corresponds to large mismatch $q$, the system becomes tantamount to the
recently studied single-component lattice with two embedded sites carrying the
cubic nonlinearity. The modes undergo qualitative changes with the variation of
$q$. In particular, at $l\geq 2$, the symmetry-breaking bifurcation (SBB),
which creates asymmetric states from symmetric ones, is supercritical and
subcritical for small and large values of $q$, respectively, while the
bifurcation is always supercritical at $l=1$. In the experiment, the
corresponding change of the phase transition between the second and first kinds
may be implemented by varying the mismatch, via the wavelength of the input
beam. The existence threshold (minimum total power) for the symmetric modes
vanishes exactly at $q=0$, which suggests a possibility to create the solitary
mode using low-power beams. The stability of solution families also changes
with $q$.
