We present detailed simulations of kilonova and GRB afterglow emission originating from black holeneutron star (BH-NS) mergers. We present kilonova luminosity function and discuss the detectability of kilonova and GRB afterglow in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity follow-up observations, and blind searches in time-domain survey observations. The predicted absolute magnitude of the radioactive-powered BH-NS merger kilonovae at 0.5 day after the merger falls in the range of [−10, −15.5]. The simulated luminosity function contains the potential viewing angle distribution information of the anisotropic kilonova emission. We simulate the GW detection rates, detectable distances and signal duration, for the future networks of 2nd, 2.5th, and 3rd generation GW detectors. BH-NS mergers tend to produce brighter kilonovae and afterglows if the primary BH has a high aligned-spin, and the NS companion is less-massive with a stiff equation of state. The detectability of kilonova emission is especially sensitive to the spin of the primary BH. If primary BHs typically have a low spin, the electromagnetic (EM) counterpart of BH-NS mergers are hard to discover. For the 2nd generation GW detector networks, a limiting magnitude of m limit ∼ 23 − 24 mag is required to detect the kilonovae from triggered BH-NS mergers even if BH high spin is assumed. This could provide a plausible explanation for the lack of kilonova detection from BH-NS candidates during LIGO/Virgo O3 (early 2nd generation detectors): either there is no EM counterpart (plunging events), or the current follow-up observations are too shallow to make a detection. On the other hand, these observations may still have the chance to detect the on-axis jet afterglow associated with a shortduration gamma-ray burst or an orphan afterglow, if the line of sight is not too far away from the jet axis (presumably the axis of binary merger). In future GW detection eras, more remote GW signals can be detected, but their associated kilonovae are more difficult to detect. Follow up observations can in any case detect possible associated sGRB afterglows, from which kilonova signatures may be studied. For time-domain blind survey observations, a high-cadence search in redder filters is recommended to detect more BH-NS merger kilonovae and afterglows in the current and future GW detection eras.