We perform a comprehensive analysis of dark matter (DM)-admixed hybrid stars, combining a bosonic DM equation of state (EOS) with a well-constrained hybrid star matter EOS, in which the hadron phase and the quark phase are described by the improved isospin- and momentum-dependent interaction (ImMDI) model and the SU(3) Nambu-Jona-Lasinio (NJL) model, respectively. All EOSs considered satisfy the causality condition, ensuring the physical viability of our models and DM interacts with ordinary hybrid star matter only via gravity. Based on a wide parameter space of DM particle mass and DM fraction, we find that for heavy DM particles, DM remains concentrated in the stellar core, reducing the maximum mass, canonical radius $R_{1.4}$, and tidal deformability ${\mathrm{\Lambda }}_{1.4}$. For light DM particles, DM forms an extended halo, enhancing these quantities, particularly for $m_{\mathrm{DM}}\lesssim 0.1\mathrm{GeV}$. Within this scenario, several massive compact objects, including GW230529_18150, PSR J0952-0607, and the secondary component of PSR J0514-4002E may be naturally explained as DM-admixed stars. Furthermore, peculiar stars with normal optical radii but anomalously large tidal deformabilities could provide unequivocal signals for the presence of DM. Future gravitational-wave and multimessenger detections can constrain DM properties and identify its presence in compact stars.

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• Nuclear astrophysics