  We present a comprehensive investigation of the electronic structure,
magnetization, specific heat, and crystallography of TbSi (FeB structure type)
and TbSi$_{0.6}$Ge$_{0.4}$ (CrB structure type) compounds. Both TbSi and
TbSi$_{0.6}$Ge$_{0.4}$ exhibit two antiferromagnetic (AFM) transitions at
T$_{\rm N1}\approx$ 58~K and 57~K, and T$_{\rm N2}\approx$ 36~K and 44~K,
respectively, along with an onset of weak metamagnetic-like transition around
6~T between T$_{\rm N1}$ and T$_{\rm N2}$. High-resolution specific heat
(C$_{\rm P}$) measurements show the second- and first-order nature of the
magnetic transition at T$_{\rm N1}$ and T$_{\rm N2}$, respectively, for both
samples. However, in the case of TbSi, the low-temperature (LT) AFM to
high-temperature (HT) AFM transition takes place via an additional AFM phase at
the intermediate temperature (IT), where both LT to IT AFM and IT to HT AFM
phase transitions exhibit a first-order nature. Both TbSi and
TbSi$_{0.6}$Ge$_{0.4}$ manifest significant magnetic entropy changes ($\Delta
S_{\rm M}$) of 9.6 and 11.6~J/kg-K, respectively, for $\Delta \mu_0H$=7~T, at
T$_{\rm N2}$. The HT AFM phase of TbSi$_{0.6}$Ge$_{0.4}$ is found to be more
susceptible to the external magnetic field, causing a significant broadening in
the peaks of $\Delta S_{\rm M}$ curves at higher magnetic fields. Temperature
and field-dependent specific heat data have been utilized to construct the
complex H-T phase diagram of these compounds. Furthermore,
temperature-dependent x-ray diffraction measurements demonstrate substantial
magnetostriction and anisotropic thermal expansion of the unit cell in both
samples.
