The controlled islanding problem is typically considered only for pure ac power systems, with the ultimate objective of either minimising power imbalance or power-flow among islands. However, as ac/dc hybrid power systems are becoming popular worldwide, current controlled islanding schemes should be redesigned to take into account the presence of high-voltage dc (HVDC) links, possibly connecting different islands. Accordingly, in this study, the authors solve the classic islanding problem combining HVDC power modulation with the conventional ac cutset search. The flexibility of the HVDC allows the authors' strategy to jointly capture the previously mentioned objectives, and provides even lower power imbalances than the minimum imbalance strategy, at a relatively small cost of increasing power-flow impact. Then, the optimisation problem is formulated as a mixed-integer linear programming problem, which can be conveniently solved with existing commercial solvers. Finally, they validate their proposed strategy in two case studies, corresponding to a modified IEEE-118 system and to the China Southern Power Grid system. In both cases, dynamic simulations show that their proposed approach outperforms classic algorithms where the presence of HVDC power modulation is not explicitly taken into account.