The development of proof methods for defeasible description logics (DLs), following those for classical DLs, is mainly based on semantic tableaux.However, the literature offers equally viable alternatives for automated theorem proving, such as the connection method.It consists of a goal-oriented direct proof search method that searches for connections (complementary pairs of literals) in a set of literals organized in clauses called a matrix.This paper presents a connection method for an exception-tolerant family of DLs.In that regard, (i) we use the language of ALCH extended with a typicality operator on concepts and another one on roles; (ii) we revisit the definition of a matrix representation of a knowledge base and establish the conditions for a given axiom to be provable from this matrix with a new normal form (Bi-Typicality Normal Form); (iii) we show how to handle term unification and define a suitable blocking condition in the presence of typicality operators; and (iv) we establish correctness, completeness, and termination of our algorithm.