  We state combinatorial formulas for hyperoctahedral group ($\mathfrak B_n$)
character evaluations of the form $\chi( {{\widetilde
C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1))$, where ${{\widetilde
C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1) \in \Bbb Z[\mathfrak
B_n]$ is a type-BC Kazhdan-Lusztig basis element, with $w \in \mathfrak B_n$
corresponding to simultaneously smooth type-B and C Schubert varieties. We also
extend the definition of symmetric group codominance to elements of $\mathfrak
B_n$ and show that for each element $w \in \mathfrak B_n$ above, there exists a
BC-codominant element $v \in \mathfrak B_n$ satisfying $\chi( {{\widetilde
C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1)) = \chi( {{\widetilde
C}_v}^{\negthickspace\negthickspace BC}\negthickspace(1))$ for all $\mathfrak
B_n$-characters $\chi$. Combinatorial structures and maps appearing in these
formulas are type-BC extensions of planar networks, unit interval orders,
indifference graphs, poset tableaux, and colorings. Using the ring of type-BC
symmetric functions, we introduce natural generating functions $Y( {{\widetilde
C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1))$ for the above
evaluations. These provide a new type-BC analog of Stanley's chromatic
symmetric functions [Adv. Math. 111 (1995) pp. 166-194].
