Let \(\Gamma\) be a compact, connected, and non-singleton set in the complex plane having connected complement. Then the Faber polynomials \(F_n(\Gamma, \cdot)\) of degree \(n\) with respect to \(\Gamma\) are defined. If \(f\) is a function holomorphic on a domain \(\Omega \supset \Gamma\), then \(f\) has a unique Faber series expansion \[ f(z)=\sum_{n=0}^\infty c_n(f, \Gamma) F_n (\Gamma, z) \] with corresponding Faber coefficients \(c_n(f, \Gamma)\). While the Faber series converges locally uniformly to \(f\) on a neighborhood of \(\Gamma\), it typically diverges outside of \(\Omega\). The function \(f\) is said to have a universal Faber series with respect to \(\Gamma\), if the divergence outside of \(\Omega\) is maximal in the following sense: For every compact set \(K\) with connected complement and every function \(g\) continuous on \(K\) and holomorphic in the interior there is a subsequence of the Faber series converging uniformly to \(g\) on \(K\). It is known that in the case of simply connected domains \(\Omega\), generically, functions \(f\) holomorphic on \(\Omega\) have this property for all \(\Gamma \subset \Omega\) as above. The main result of this paper shows that the same is true for doubly connected domains \(\Omega\) being the complement of a compact and connected set.