[Infidelium ]. In a non-Christian country. A “bishop in partibus” means a bishop in any country, Christian or otherwise, whose title is from some old see which has fallen away from the Catholic faith. Thus, in England, the Bishop of Cisamus, the Bishop of Emmaus, the Bishop of Amyela, are bishops in partibus. Dr. Wiseman was Bishop of Melipotamus before he was Archbishop of Westminister. A bishop in partibus does not mean a bishop in a land of infidels; he may be so, but this would not make him a bishop in partibus.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894