  The detections of gravitational waves (GWs) from binary neutron star (BNS)
systems and neutron star--black hole (NSBH) systems provide new insights into
dense matter properties in extreme conditions and associated high-energy
astrophysical processes. However, currently information about NS equation of
state (EoS) is extracted with very limited precision. Meanwhile, the fruitful
results from the serendipitous discovery of the $\gamma$-ray burst alongside
GW170817 show the necessity of early warning alerts. Accurate measurements of
the matter effects and sky location could be achieved by joint GW detection
from space and ground. In our work, based on two example cases, GW170817 and
GW200105, we use the Fisher information matrix analysis to investigate the
multiband synergy between the space-borne decihertz GW detectors and the
ground-based Einstein Telescope (ET). We specially focus on the parameters
pertaining to spin-induced quadrupole moment, tidal deformability, and sky
localization. We demonstrate that, (i) only with the help of multiband
observations can we constrain the quadrupole parameter; and (ii) with the
inclusion of decihertz GW detectors, the errors of tidal deformability would be
a few times smaller, indicating that many more EoSs could be excluded; (iii)
with the inclusion of ET, the sky localization improves by about an order of
magnitude. Furthermore, we have systematically compared the different limits
from four planned decihertz detectors and adopting two widely used waveform
models.
