Step 1: Recall the androecium of Fabaceae.
In family Fabaceae, the stamens are generally
\[
\boxed{\text{diadelphous }(9+1).}
\]
The anthers are
\[
\boxed{\text{dithecous}.}
\]
Step 2: Compare with other families.
\[
\begin{aligned}
\text{Fabaceae} &\rightarrow \text{Diadelphous stamens}
\text{Solanaceae} &\rightarrow \text{Epipetalous stamens}
\text{Liliaceae} &\rightarrow \text{Epiphyllous stamens}
\end{aligned}
\]
Thus, the characteristic specific to Fabaceae is
\[
\boxed{\text{Diadelphous and dithecous anthers}.}
\]
Step 3: Choose the correct option.
Hence, the correct option is
\[
\boxed{(C).}
\]