Black holes (BHs) in an inspiraling compact binary system absorb the gravitational-wave (GW) energy and angular-momentum fluxes across their event horizons and this leads to the secular change in their masses and spins during the inspiral phase. The goal of this paper is to present ready-to-use, post-Newtonian (PN) template families for spinning, non-precessing, binary BH inspirals in quasicircular orbits, including the PN and PN horizon-flux contributions as well as the correction due to the secular change in the BH masses and spins through PN order, respectively, in phase. We show that, for binary BHs observable by Advanced LIGO with high mass ratios (larger than ~10) and large aligned-spins (larger than ), the mismatch between the frequency-domain template with and without the horizon-flux contribution is typically above the mark. For (supermassive) binary BHs observed by LISA, even a moderate mass-ratios and spins can produce a similar level of the mismatch. Meanwhile, the mismatch due to the secular time variations of the BH masses and spins is well below the mark in both cases, hence this is truly negligible. We also point out that neglecting the cubic-in-spin, point-particle phase term at PN order would deteriorate the effect of BH absorption in the template.