  We consider the standard modules of rectangular highest weights of affine Lie
algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex
algebraic techniques we construct the combinatorial bases for standard modules
and their principal subspaces and parafermionic spaces. Finally, we compute the
corresponding character formulae and, as an application, we obtain two new
families of combinatorial identities.
